I'm a male feminist university student, although I have only recently been forcing my eyes open to the real damage that patriarchal sexism does to women. However, as soon as I resolved to myself to confront societally imposed sexist ideas wherever I meet them, I find my girlfriend repeating them to me. This consists of emphasizing sexist gender-role stereotypes, like giving me her card to pay for a meal so that she isn't seen to be forward or acquiescing demurely to my suggestions despite me asking for (and statistically equally acquiescing to) her suggestions or opinions on things. She makes comments on how other women are "sluts" to be dressed in a certain manner, and says "it's different for men!" when I debate this with her.
Now, if she were a man, I wouldn't hesitate to confront the internalized sexism that she doesn't seem to be aware of. However, I don't want to overstep my place in the feminist movement—which most people tell me is in educating and confronting men, while leaving women to do the same with women. I think the power relationship is even more messed up because she sees it as part of her "duty" to go along with what I say, and I don't want to use that mechanism to gain her agreement with an ideology if she’s totally opposed to such an idea.
What should I do? I love her and want her to be able to liberate herself from internalized sexism, but I don't want to commit the classic male feminist mistake of feeling entitled to barge in and lay down the law.