1. If men want to take more responsibility for creating or not creating life, their options are far easier than women's'. Wear a condom, get a vasectomy, be more selective about who they're having sex with rather than trying to bang every woman they can. Few men do any of these things.
2. You've for some myopia of your own you can't see past. The thing about cuckolding men into caring for children who are not theirs happens, but in far far less numbers than your comment would have us believe. Life isn't a Heart song. Far more women are left to raise unwanted children while the man skips on off to his next bang than men getting stuck with children who aren't biologically theirs unknowingly.
3. The cost/benefit return for male birth control methods in terms of both financial costs and the cost of side affects should make men jump at the chance to embrace the definition of masculinity by protecting women .... from them and the unwanted pregnancies they bring with them. Isn't it funny how men are always yammering on about being providers and protectors and that's what makes them a man. Given an actual opportunity to do just that and you get a lot of crickets, dust clouds kicked up from where they run and hide, or hilarious outrage on behalf of their member who's suddenly feeling a little shrivelled.
4. Although medical advancements have made childbirth and pregnancy safer than it's ever been, things still go wrong. When they do, it is the woman who is imperiled, not the man. So let's not pretend like anything detrimental to the male is anywhere near equivocal to what women face in terms of their life changing. It's not.