Mutually Exclusive Magic

""Since Light and Shadow cannot coexist, possessors of Shadow Magic must first give it up before learning this [Light] magic.""

- Saga Frontier

In a fantasy setting, where magic is abundant, a commonly seen rule is that no one can master multiple or opposing schools of magic-- One can either learn divine or unholy magic, but not both.

The reasons for this may vary. It may be that the teachers of either school don't particularly get along very well, it may be that the talent for any given type of magic is an inherited trait, or it may simply be that all you used to learn one type contradicts what's used to learn the other, and most people just can't get over that hump. In some settings, this extends to all forms of Functional Magic: Hermetic Magic, Psychic Powers, Ki-powered Supernatural Martial Arts, etcetera.

Depending on the series, it may still be possible to learn multiple schools, so long as they don't oppose each other-- One can learn Fire and Wind magic together, but not Fire and Water.

Breaking this forced division is the source of the power of a Yin-Yang Bomb. The Red Mage averts this restriction.

Anime and Manga

 * Bleach has Hollow and Soul Reaper powers. Technically, they're supposed to be polar opposite types of abilities, but certain characters have gotten around these limitations. The Arrancar are Hollows with Soul Reaper abilities, while the Vizard are Soul Reapers with Hollow powers.
 * Kenichi: The Mightiest Disciple has Sei and Dou ki. They can be mixed, it just causes horrible internal damage and fun stuff like your eyes possibly rupturing. Borderline example as they both basically do the same thing anyway.
 * In Mahou Sensei Negima, Ki and magical power are opposite, and trying to use both at once usually ends with Stuff Blowing Up. However, Negi himself gets around this by using magical power as a substitute for Ki in his martial arts techniques while still using it to power his spells as well. Additionally, there's a special technique which synthesizes Ki and magic, but it's notoriously difficult and only three characters are known to have ever done it, ever.
 * Esper powers and magic in To Aru Majutsu no Index. If an esper uses magic, his enhancements get in the way and cause massive hemorrhaging. Magic is said to have designed for people who weren't born with esper abilities. One esper in the series is able to use magic anyway because his esper ability happens to be a mild Healing Factor.
 * Tsukihime / Fate Stay Night have magic and powers from Gaia counteracting each other. Humans are cut off from Gaia specifically because of their development of Magic Circuits. Arcueid uses her Marble Phantasm to create even more powerful effects than magic can, but is highly dependent on her surroundings and is also limited to effects that can happen in nature. You simply can't use both systems. However, the Church's divine powers do work with magic and are partially based on it.
 * Clow in Cardcaptor Sakura was able to combine Chinese and Western magic, which were previously thought to be incompatible.

Fan Fiction

 * In Shinji and Warhammer 40 K, psychic energy and the AT-field oppose each other.

Literature

 * The entire plot of Master of the Five Magics by Lyndon Hardy is a subversion of this trope. No one in the world believes that anyone can learn more than one type of magic, but Alodar not only learns the basics of all five, he manages to combine them.
 * A similar thing happens to Pug/Milamber over the course of the many Riftwar Cycle books. Having studied, at first unsuccessfully, under a practictioner of 'lesser' magic, he finds it much easier with 'greater' magic, but later is able to use both, as well as elven magic and more, saying that in fact magic is just magic, and the only limitations lie with the user. That is, most people find they can only go down one path, but some can handle more.
 * In John C. Wright's Chronicles of Chaos, the types of magic run on immiscible paradigms. To even understand how another person's magic work, you would have to think the same way, which would stop you thinking your way, and so you would lose your paradigm's magic.
 * The Old Kingdom series (Sabriel and its sequels) has Charter Magic and Free Magic. Charter Magic is the more organized and academic sort of magic. Magical creatures found in nature and anything to do with the Dead are Free Magic. The only person who practices both is the Abhorsen.
 * Since the eponymous Chrestomanci has the job of overseeing all forms of magic use, his training requires that he learn about all of them, and preferably how to do them. However, candidates for the post are chosen for their strong natural talents as an Enchanter, and they find it extremely difficult if not impossible to perform magic in a way not natural to them. This is mostly because Enchanter magic shortcuts past most of the annoying parts, so when trying to do magic in another way an Enchanter is forced to take unnecessary steps.
 * In the Apprentice Adept series, though magic is derived from a single source - Phazite - there are many mutually exclusive ways to invoke that magic: Protagonist Stile (The Blue Adept) utilizes rhyming spells and music, Adept Yellow uses potions, Red uses amulets and talismans, White uses runes and sigils, etc. The only exception is if someone is using the Book Of Magic, which gives even non-humans Adept-level power in ALL the disciplines.
 * In The Wheel of Time series, magic is powered by the One Power, which has male and female halves. Male and female magic-users can accomplish the same things, but more often than not by different methods. For example, the best way for a man to put out a fire is to take the heat from the fire directly but the best way for a woman to do it is to use air or water to snuff it or quench it.
 * Averted and played straight in the The Night Angel Trilogy. Kylar thinks this is true racially, as people from one country use only healing magic. Durzo explains that hundreds of years ago, those very same healers gave up Black Magic after using it for ungodly powerful things. As a result, the problem is no one will teach them how to use Black Magic in their own country, not that they can't use it. It's played staright with the existence of Male and Female specific abilities (with uncommon exceptions) and the Vir. But you don't want to know about the Vir.
 * The Saga of Recluce has order magic and chaos magic, and almost always a mage will only practice one or the other. This is because most mages channel magical energy through their bodies, and some of the energy from each spell stays behind in the body; if a mage casts a order spell and then a chaos spell, the residual order energy will react in a painful (or lethal) manner with the new chaos energy. Mages who learn how to channel energy without the energy passing through their bodies can use both types of magic, but knowledge of how to do this is rare, since both order mages and chaos mages tend to be dogmatic about their type of magic being the best.
 * In Valentin Ivashchenko's Warrior and Mage, learning the ways of the divine magic effectively prohibits the priest from learning arcane magic; non-human species don't possess divine magic. Arcane mages are born with certain affinities, referred to by color. While mages can exhibit multiple colors, e.g. red + dark blue = fire-lightning mage, there were no known black (necromancy) + anything mages.
 * As a recurring motif of modern Russian-spoken fantasy, the volhvy (Slavic pagan druids) were limited to spells and abilities of their respective deity. In settings with advancing monotheism adopting the "old way" (paganism) and adopting the "new way" (White God, Savior, Light God, various other Crystal Dragon Jesus ideas) are also mutually exclusive.
 * Vadim Panov's Secret City series of novels has several mutually exclusive schools - the white Tat', the black Nav', the red Chood', the green Lyud', the humans' Chel magic, Azatot's Golden Root magic, nature magic of the nymphs and other spirits and the Gift of the Inquisitors. In-universe exceptions exist:
 * Chel mages can use Lyud' magic.
 * The power of Galla's temples grants a single spell after joining Galla's heresy, independent of previous magical ability.
 * Geomancy. While difficult, obscure and powerful, it can be partially added or adapted into other schools; although there are only 2 such part-geomancy spells in the canon.
 * In The Secrets of the Immortal Nicholas Flamel, it's completely possible to learn all four types of magic, but only the Chosen Ones can use two at once; and, once they've learned the traditional four, they are the only ones who can learn the fifth type: Aether.
 * Averted in the Mistborn trilogy. An Allomancer burns metals to fuel superhuman abilities, a Feruchemist stores his own abilities in metals and uses them later, but it's entirely possible to inherit both.
 * Played straight in the World of Ethshar series. The primary restriction on magic-users is that the source of each type is different. Theurgists pray to gods; demonologist bargain with demons; sorcerers manipulate talismans; wizards manipulate reagents; witches manipulate their own magic; warlocks manipulate a foreign magic. Learning how to use even one school can take a lifetime so very few have the ability or interest to try and study another school.
 * It has been noted that many warlocks were originally users of other magics, but either lost the ability or interest to use their original magic during the Night of Madness.

Tabletop Gaming

 * Specialist wizards in Dungeons and Dragons cannot learn spells from their "opposition schools" (which were either fixed or chosen by the player, depending on edition). However, most mages can learn any spell; they just don't get the bonuses that specialists do.
 * While not fully incompatible, in the classic versions magical creatures and magic-users are less likely to discover psionic talents, while psonically powered creatures tend to be resistant to magic and have hard time studying it.
 * Forgotten Realms after Karsus's Folly has Weave and Shadow Weave split as two independent power sources, controlled by warring goddesses. One can't use both and when magic from both in raw form collides, it causes large-scale unpleasantness such as planar rifts. Also, Phaerimm magic and Sharn magic are so non-standard and incompattible that their spells interact violently, changing the landscape.
 * In Dragonlance magic comes from the trio of moon gods, and while it's not technically incompatible, the leading wizardly organization enforces the split into three Orders.
 * In Shadowrun you could be a hermetic mage or a shaman but not both, because their mindsets were so different. As more magical traditions were introduced, they all (as far as I can remember) followed this rule. In later editions you could mix the physical adept (magical martial artist) with spellcasting, though.
 * Thaumaturges from the New World of Darkness supplement ''Second Sight' can only practice one magical tradition at a time. Changing is possible, but you forget all your previous spells doing so, even if the tradition you move to has an equivalent.
 * In Exalted, Sorcery and Necromancy are opposed, being based on manipulating Creation's living Essence and the Underworld's entropic Essence respectively, and any given Exalt type will have a higher affinity for one or the other, having access to spells one circle lower for their tier in the case of their lower affinity.
 * Infernals of both types (Green Sun Princes and Akuma) are unable to learn sorcery in the standard sense (that is, as normal Exalts of their type). Instead, their sorcery is channeled through initiation charms specific to each Yozi, which has limits and enhancements on the types of magic they can perform.
 * Alchemicals are unable to use either sorcery or necromancy, but instead have access to another kind of magic called Pattern Weaving, which only they can use. It is possible for them to access sorcery and necromancy, but only by using Voidtech and sacrificing their knowledge of Pattern Weaving.
 * In several Palladium tabletop RPGs, but most explicitly in Beyond the Supernatural, psychic powers require the permanent expenditure of magic energy to develop. As a result, psychics have little magic energy left over for casting spells...unless they're Mystics, who can use both.
 * A general rule in Unknown Armies. Becoming an adept requires an insane devotion or obsession with a concept or school of thought, and that sort of focus can never be divided. Becoming an avatar requires that a character follow the specific mindset of an archetype, almost all of which are mutually contradictory. Very rare individuals can juggle both avatar and adept obsessions, or multiple weaker adept obsessions, but the results tend to be so far off the crazy charts that they're closer to forces of nature than characters.
 * In Aberrant and Trinity, the same genetic predisposition gives rise to Novas and Psions, but the energies involved interfere with each other. Not only can an individual use only one type of power, but a Nova and Psion in close proximity will actually interfere with each other's powers.
 * In Age of Aquarius, magic schools are based on sets of belief, and that's why you have a hard time trying to combine belief in Goetic demons, for example, and Viking gods to mix Hermetic and Runic magic. It's possible to believe in an All Myths Are True world in this setting, but it will result in a really weak form of Post Modern Magic.
 * The Warhammer Fantasy Battle universe has magic powered by the 8 Winds of Magic. It's not impossible to use spells powered by different (or even multiple) Winds, but unless you're an elf, or some form of Chosen One, Bad Things tend to happen. Intriguingly, Rainbow Wizards tend to have serious trouble learning and casting spells from the Lore/Wind in opposition to their own, while High and Dark Wizards don't have this problem, no matter which Lore they originally learnt.

Video Games

 * In Saga Frontier, One can master Light OR Shadow magic, Arcane OR Rune, Time OR Space, Realm OR Mystic, and Mind OR Evil. The one exception is Blue, who gains his twin brother's magic after the Wizard Duel between them. If you buy magic in an opposing school, you'll forget all the spells you knew.
 * This has been a staple since the Romancing SaGa Trilogy: you can only learn only half the magic spells. In Romancing SaGa 2, however, you can combine specific elements if they are not opposite to each other to create new and more powerful spells.
 * In the storyline of the Warcraft universe, Priests cannot use both Holy and Shadow spells, but this is averted in World of Warcraft due to game mechanics. Priests in the game still can't use them both well at the same time, since they'll need to specialize.
 * Shadow Priests that are in Shadowform can't cast Holy spells at all, they force you out of Shadowform. There's no restriction for the healing specs to cast Shadow spells though.
 * Most Warrior abilities require a certain stance to use, meaning that while they can use abilities more in tune with their other specializations, they would have to switch to use it, which prevents them from using the abilities most vital to their role until they switch back.
 * In Master of Magic you cannot learn spells from both the Life and Death magic schools. All the others can be combined, (and these two can be combined with any of the other three schools) but not these two.
 * Unreal Tournament has a mod/gametype called U 4 E Fortress. One of the classes in this mod is the Wizard, which unlike the other classes can level up and gain spells from eight different schools (think Constant Warriors Linear Wizards). When the Wizard first learns a spell from a school, a selection of other schools becomes Lost Forever. However, some servers allow all spell schools after a certain level.
 * Many Final Fantasy games that have job classes normally have classes that are only able to use one magic type, such as black mages and white mages using Black and White Magic, respectively. This gets muddled, however, in games like Final Fantasy V, Final Fantasy Tactics, and Final Fantasy XI that allow you to use secondary abilites from a class you've previously worked on. It should be noted, of course, that games like Final Fantasy X throw all this out the window and give everyone the potential to learn anything, certain attacks aside.
 * There's also Red Mages, who can learn both white and black spells, but not as well as the ones who specialize in them.
 * Played straight lorewise in the Final Fantasy IV universe, where people capable of casting both white and black magic are called "sages" and are exceedingly rare. Rydia begins with the ability to cast black and white magic in addition to her summons, but when she returns to your party, she sacrifices her limited white magic to use black and summoning magic to their fullest potential.
 * In Age of Wonders your leader can choose only non-antagonistic magic spheres.
 * In Age of Wonders 2, you can either choose all of them, giving your a random selection that often ends up game-breakingly good or bad, or a single sphere. Notably, no matter which you choose, you can still buy/find/receive any spell. Also, Common sphere spells always can be researched and Secret sphere never.
 * In Age of Wonders: Shadow Magic, you can either pick a single school or massively gimp yourself by taking multiple schools, ensuring that you never get any powerful spells.
 * Starcraft: Protoss have the high templar ("light") and the dark templar, separated millenniums before the start of the game. One of the main heroes eventually learns to use both types of power and use it to defeat the Big Bad (the first one, anyway). It's insinuated that only an extremely exceptional individual is able to pull this off.
 * Variation in Knights of the Old Republic. Jedi can use Sith powers, and vice-versa, but suffer a penalty to the spell cost (and likewise a bonus to more properly aligned force powers). They're not completely exclusive, just more costly.
 * Jedi Knight's Karma Meter is more strict. At a certain point of the game, it checks the tally and locks out the opposite alignment powers. Any points you invested in those are Lost Forever.
 * Meridian 59, the first "3-D" MMORPG, allowed you to master only one type of magic at a time. You could become somewhat decent at another one. But mastering another type meant you became less powerful in the other.
 * In Mabinogi, the Dark Knight transformation is incompatible with the Paladin transformation. However, there is also a story-reason for this as well as magical incompatibility: the choice one makes to become a Dark Knight would make one unable to access the Paladin transformation anyway.
 * In Jade Empire, you must choose between Fortune's Favorite and Golden Star, and Ice Shards and Dire Flame in Act I, but can buy the other later. In Act II, however, you can get Stone Immortal if you are far enough on the Open Palm end of the spectrum and Tempest if you are far enough on the Closed Fist, and have no opportunity to get the other.

Western Animation

 * In Avatar: The Last Airbender and The Legend of Korra, the ability to bend one of the four elements (water, fire, earth, and air) is mutually exclusive. Mixed-heritage people take after one side or the other (or possibly neither). The one exception to this rule is the Avatar, who is able (and required) to master all four elements. Even then, there's a spiritual or philosophical divide between the techniques used for each element - Aang was raised an airbender, which is all about flowing with the surroundings, and had trouble with the stubborn assertiveness that earthbending required. In contrast, Korra's brash and hotheaded and has serious problems grasping airbending due to its go-with-the-flow philosophy being so opposed to her own temperament.
 * In Teen Titans when Larry breaks his finger that lets him rewrite the rules of reality, Raven says she can't use her magic to heal it since combining their two powers could create an Earthshattering Kaboom.
 * Mixing different schools of magic in Aladdin is highly dangerous. This was frequently used, besides his diminished power, to keep Genie from being able to fix things too easily.