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Misogyny **DOES NOT** refer to hatred of women. It refers to a social construct made to enforce patriarchy. In other words it doesn't refer to the feelings of an individual. It refers to a prejudicial view against women at a *societal* level. It is used to identify and address a social phenomenon and it's context is always necessarily structural.
The word "misandry" is weaponized to decontextualize the word "misogyny". It refers to the sentiment of individuals to imply that misogyny does the same. It attempts to reframe a discussion of a function of society as merely a discussion about individual bad actors. It moves culpability for the systemic oppression of women from the shoulders of society as a whole to an ill-defined, ever shifting nebulous cloud of individuals. An impossible target. It perverts feminism from an attempt to reframe social norms to an infinite unwinnable game of whack-a-mole. That is the purpose of the word misandry.
If misandry were truly a *good faith* counterpart to misogyny it would refer to a social construct made to enforce matriarchy. It's context would always be necessarily structural. But it's not. It never is. When people say "misandry isn't real," they aren't saying no individual ever hates men simply for being men. They are saying that equating individual hatred of men to systemic prejudice against women is a false equivalency. "Misandry" is a weapon of patriarchy intended to pervert and neutralize any attempt to identify the structural nature of misogyny and patriarchy.