Binary Characterization Assumption

On the gripping organized crime show For A Few Murders More, Don Smith has a beautiful daughter, Tropina, that he's tried to raise completely unaware and innocent of his life of crime... he wants her to have a normal life and never enter his world of murder, theft, and lawlessness. But Don Smith's hated (and much younger) rival Don Jones meets Tropina, and engages in a romance with her that threatens to drag her down the path of being a gangster's wife. Don Smith, enraged, has Don Jones dragged before him to be executed by his own hands. In their final faceoff, Don Smith rages that he's doing this to protect his little girl. Don Jones sneers back that Don Smith has always just hated him for being a younger, more vital rival, and Tropina's just the excuse. Bang goes the gun, thud goes Don Jones' body, fwoosh go the online forums.

A Broken Base immediately ensues over just why Don Smith killed Don Jones. Was it like Don Smith said, was he just doing his best to be a good father and keep Tropina from turning to a life of crime? Or was it like Don Jones said, was it just an act of hatred and petty jealousy that had nothing to do with Tropina at all? Each character's fans line up and being the war, and neither side stops to think that maybe both are true.

Humans are complicated creatures, and sometimes writers do their best to reflect that. In this fictional example, it's entirely possible that Don Smith's primary motivation really was to protect Tropina from a bad influence... but the fact that the bad influence was a man he already hated may certainly have influenced his course of action. Alternately, maybe Don Smith really was just looking for an excuse to rub out Don Jones... but at the same time he really was concerned for Tropina.

Binary Character Assumption is what happens when the audience assumes that a character can only have one, single motivation for anything they do. When presented with multiple possible viewpoints for who a character is or why they did what they did, it's simply assumed that one of them must be the right one and all others must be wrong. The character is either a Complete Monster or an Anti-Villain, they're either a Lawful Good Knight in Shining Armor or a Lawful Evil Knight Templar, they're either a Pragmatic Villain Well-Intentioned Extremist or a Card-Carrying Villain doing it For the Evulz.

In short, this trope is what happens when the audience makes an assumption that the character is a Flat Character when the more direct interpretation of their actions would be that they're a Rounded Character.

Anime and Manga

 * Irresponsible Captain Tylor: Justy Ueki Tylor is an in-universe example. Some think he's a genius tactician and employer of Obfuscating Stupidity; others think he's a lucky idiot.
 * Tenchi Muyo! Ryo-Ohki: Two decades after the episode was first released, there's still debate amongst the fan base as to why Washuu-chan did what she did to Ryoko in the bonus material at the end of episode 13. Giving specifics would involve spoilers.

Comic Books

 * Does Batman fight crime because he wants to protect people and doesn't want others to feel the pain he's felt, or is he just an angry psycho out to get violent revenge on criminals? The war between these two characterizations has been going on both in the fandom and among the writers for a good long time. A more human take on it would be that someone can have noble goals that came out of tragedy while still feeling a lot of anger about said tragedy.
 * Almost the exact same thing plays out with The Punisher, where both fans and writers seem to assume that if Frank is truly a violent man who enjoys killing criminals, it must mean he never really loved his family and is secretly glad they're dead, as opposed to just killing criminals because he loved his family so much and was driven to vigilantism by their loss. Logic would seem to say that maybe Frank is an innately violent man who probably does enjoy killing (bad) people, but that doesn't mean he didn't love his family and doesn't hate that they died.

Live-Action TV

 * Breaking Bad: Did Walter White do it all for his family, or was every action he took due to selfishness and greed? The more nuanced interpretation, that Walter did care about his family and did want to make sure they were taken care of, but was also driven by inner demons that cried out for recognition and power, is largely ignored.

Real Life

 * Any politician who had to implement an unpopular measure. The politician's supporters will tell you the politician did what needed to be done; the politician's opponents will tell you the politician ignored the will of the people. There are plenty of examples - the Rule of Cautious Editing Judgment implies we shouldn't single out any of them here.