Because Everyone has their own definition.
A Controversial Definition Trope is a trope that is multivocal. That means that while everyone knows the meaning of the concept in a wide sense. No one has a precise “objective" definition because everyone has their own definition of the term. Even if an objective definition is given, most people will try to impose their own particular interpretation of the concept regardless of the situation. Mainly because everyone has very strong opinion of what the concept in question should mean.Therefore any attempt at one " true definition" or wheter or not it applies to that particular definition in a given moment will be a source of debate. The best example is probably Mary Sue. Everyone knows that a Mary Sue is in a broad sense a "perfect character in-universe". However trying to define it with specific criteria is a Berserk Button for many, and therefore impossible to define by any objective means. For example Whether or not a certain character is a Complete Monster or whether or not a Mary Sue can be a "good character" will depend on each person perception an interpretation of the conpet. In other words the issue will be on the language and not in the events that trope is trying to define. Differs from with Subjective Trope depending on the context of the situation. While a Subjective Trope definition may be clear and even completely accepted. The issue for a SubjetiveTrope will be whether or not it applies to a given situation (people will perceive the things differently). Whereas in an Controversial Definition Trope the issue won't be on the situation (Everyone could perceive the situation exactly the same), but on the definition of that situation.
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