How do you deal with the hatred young women seem to have against us right now?

Seriously. I would consider myself a feminist, at least in the old definition of the word. I believe in equality for men and women. I do think we are generally different, but that no one sex is above the other. However, as a young man in STEM in university right now, I am constantly faced with hatred just for existing as a "straight white cisgender man".

A female friend, who gets free rides from me to school in my car all the time (she is a lesbian and NOT my type at all so I'm giving her rides because she is/was a bro, not out of any kind of desire for her) was absolutely trashing men in my car the other day. I told her she was being sexist. She said sexism only applies to women being treated badly. I said no it doesn't, that's systemic sexism, sexism is just hating one sex. Well, apparently, that's "mansplaining sexism".

She also told me men are incapable of forming genuine friendships lol. I did not take kindly to that. She said unless I admit I'm wrong and men are trash that she is ending the friendship. Obviously I'm not going to tell her I was wrong, because I'm not. But jesus, we were good friends for a year or so I thought. The world is insane right now. How do you deal with still being expected to give endlessly while also being told to suck it up and deal with the hate? I'm genuinely considering not having female friends for a while due to the culture right now, even though I wholeheartedly believe men and women are capable of being friends.

Edit: I am at a Canadian uni and this is actually the sentiment of most of the women I've talked to in my program. Not joking. This one just hurts cuz it comes from someone I thought was a friend, but it is certainly not a one-off.