The goal is for everyone to be treated equally, not just women. People tend to create an us-vs-them mentality and form tribes, especially when they feel they're under attack. Much of the online backlash against feminism is due to militant, insulting forms of it that are popular on sites like tumblr that trigger this us-vs-them mentalities. That severely degrades the image of feminism when it seems to be anti-white guy. You can't allow sexism as long as it's against white men. If you do, you're part of why feminism is stalling.

"Mansplaining" doesn't oppress you like "PMSing" doesn't oppress women, which it does. It reinforces negative stereotypes and forms potentially false assumptions. Just because other people say mean things about women doesn't mean you should say mean things about men.