Basically what most feminists will argue is that the man chose to have sex, so he has to take responsibility for "funding" the child's upbringing. Society should not have to pay for it. Thus child support. Here's the kicker: Most, or probably all, feminists will argue that when a woman gets pregnant her career suffers, and this is an unfair consequence that only affects women. Hence society should somehow equalize this. But wait, the woman chose to have sex too, isn't she responsible for the consequences? So obviously there is a double standard at work here. Point this out and you should force them to either chose one or the other or display their hypocrisy/misandry in plain sight.

I hope this can be useful in future debates.