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To what extent is "destroy the patriarchy" a red herring to get people angry at "men" rather than "sociopathic billionaires of all genders?"

Very little. The patriarchy is not about "men better than women," but about enforcing rigid social roles that restrict everybody. Men are expected to show strength, be emotionless, and give their lives in the pursuit of social status far more than women. They are then brainwashed by the power they hold over women into thinking this is a good thing, all the while making us all less free.

This dynamic is so powerful and so prevalent that it is the single greatest social strategy the oligarchs have access to. Every fascist movement on earth succeeds or fails depending on how well they exploit men's place in the patriarchy. The problem with patriarchy lies not in who wears the crown, but how it turns average men into loyal foot soldiers.

On the other hand, women like JK Rowling reinforce their own oppression, as do the actually toxic women who spend all their time hating men. They ostracize other women for not meeting their standards while viewing relationships with men as purely transactional and oppositional. Transphobia is common as they seek to make rigid distinctions between themselves and men. In doing this they cement their roles in society, which only serves both patriarchy and oligarchy.

So no, destroying the patriarchy is not a distraction from class war, but an essential part in winning it. It has nothing to do with hating men, and the myth that it does is propaganda that only serves hierarchy.