I am not sure that most women are true feminists. I don't think most women want equality. Don't get me wrong, I think that women want to be treated with respect, have equal pay for equal work, want family leave, and want the sexist bores to be slapped down. I want that for them and all of us. I think some of them enjoy the privileges they have and don't mind so much the disadvantages of living in a patriarchy. I think many feminists want their cake and to eat it too.
I don't imagine that we will see it, men saying no, happening a lot more. Yes, men will decline, men have always declined but only in moderate numbers. The only way it will happen more is if women initiate a whole lot more and face a whole lot more rejection. I just don't see that as likely.