> There's a side component of the mens right advocacy movement that tries introducing the idea that there's some flaw in woman's rights movements because they're not true gender equality movements: inter alia, famously, lawsuits over ladies nights at bars

It's not just men's rights. There is a massive part of the West who believes that to acknowledge that women are physically different than men is the real sexism. Erasing female as a distinct category entirely is supposed to be the anti-sexist option. Females are just weak men, too lazy to get taller and stronger. Or men are just big, sterile, extremely strong women. Now that I type it, I guess it is a men's rights movement.

Turning "woman-hating" into "misogynist" into "sexist" was as men's rights as turning Women's Studies into Gender Studies.

edit: always remember that the history of "sexism" is not a history of people hurting people, it's a history of men hurting women. Sexism is a euphemism. The reason only males are required to do military service in Korea is because men decided that's how it should be. If men decided otherwise, it would be changed.