Averse Adept

There is a character who is good at something. Maybe it's skill, maybe it's talent. Maybe it's both. He or she isn’t just above average at it, he/she’s good at it, possibly even exceptional.

Unfortunately their prowess is only matched by how much they dislike exercising that prowess. Of course the plot will probably put them in a situation that forces them to do it anyways.

(current title may be a bit of a misnomer. They don't have to hate that what they are skilled at exists to qualify (although they can), they just have to hate doing it).

Contrast Giftedly Bad. Folks Desperately Looking for a Purpose In Life are prone to this trope, when their dreams don't align with their talent.

Anime and Manga

 * In Naruto, a story where most characters are trained in the lethal arts and more often than not are glorified Child Soldiers  and Professional Killers, there are individuals like Haku and Itachi who don't like killing despite (or arguably because) they are exceptionally good at it.
 * In Wizard's Soul - Koi no Seisen Manaka doesn’t like playing Wizard’s Soul to win. Playing without putting effort into winning isn’t that bad though. The reason she hates trying to win is . The reason Manaka enters a tournament is because her dad ruined her family's financial situation when he fell for a scam and she thought winning money in a tournament would get them out of it.
 * Miho Nishizumi in Girls und Panzer changes schools in order to get away from an school club activity that she's good at but no longer likes. However, in what looks like bad luck, her new school's Absurdly Powerful Student Council forces her to not only join the same club at the new school but also become the club's captain.
 * The first few episodes of Trigun show that Vash the Stampede is good at defeating armies and handling villains. He also hates being a Person of Mass Destruction owing to the harm it causes, which is why he keeps traveling a lot.

Literature

 * Erin from The Wandering Inn has astonished people with her feats of violence including killing a goblin chieftain 1v1 and single handedly wiping out a nest of shield spiders. Erin actively dislikes killing. Killing things that are really stupid like flies is fine though.

Video Games

 * In Valkyria Chronicles III several potentials are setup this way to reinforce what a dysfunctional bunch the penal brigade it stars is. It seems it's also targeted to nerf Scouts since they were overpowered in the first game.
 * Riela Marcellis, who has Survivors Guilt from repeatedly being the Sole Survivor due to her initially unexplained Healing Factor. This manifests as "Angel of Death" (the title she has been given for her supposedly cursed nature) which lowers her stats when taking inception fire. Her default and favored class is Scout, which naturally takes inception fire, and said healing factor gives her a chance to heal the wounds taken from it at the end of a turn.
 * Amy Apple has the "Loneliness" potential, which lowers her Evasion (ability to avoid counter attack) when no allies are nearby. Amy's default and favored class is also Scout, which is all about running ahead of allies.
 * Valerie Aynsley has "Curiosity", which lowers Evasion upon spotting an enemy unit. Scouts have the highest vision radius and distance.

Visual Novels

 * The Danganronpa series is no stranger to students who ultimately dislike their Ultimate talents.
 * Trigger Happy Havoc has Leon Kuwada, the Ultimate Baseball Star. During Free Time Events, he mentions that he hates baseball and would rather pursue a career in music.

Western Animation

 * The DuckTales shows that Gladstone may rely on his good luck, but he hates it when he keeps winning every game in the Macaw casino. He gets annoyed when a casino attendant tells him he won two cars. It's because.
 * Downplayed in My Little Pony: Friendship Is Magic: the Cutie Mark Crusaders keep ignoring what they're good at (and could actually earn them their Cutie Marks and set the tone for their lives) in favour of trying out many other activities (which don't get them Cutie Marks).
 * Gus from Recess is a master at dodgeball, a skill that earned him the nickname "El Diablo". From when he transfers to 3rd Street School he keeps this a secret from everyone, even his friends, as he fears the harm his talent can cause. When Spinelli holds his guitar hostage to make him spill why he no longer plays dodgeball, Gus explains that during a ferocious game, he accidentally hit a kid who wasn't playing; the kid ran off crying before Gus could apologize and spent every subsequent recess inside.