It couldn't have anything to do with women risking their lives for 9 months carrying the child to birth in their bellies? Or that they tend to breastfeed their children for months after birth, which men simply can not do?
Sure, of course. It's probably both. But you do understand that men get discriminated in child custody trials even if the child is already well weened off the tit?
The point is that the situation is not created by patriarchy, but by biology. That women tend to be the caregivers is simply an extension of the beginnings (pregnancy, higher investment in bringing the child to life).
Personally I suspect that women being allowed to be the primary caregiver is actually a privilege they earn because their investment in having the children is so much higher. Feminism needs you to believe that being a stay-at-home mum is a horrible ordeal and a hallmark of oppression. The opposite is probably true, if you consider the average job. There may be jobs that are more fun than taking care of your own children, but most jobs aren't like that.
Consider a stay-at-home dad. He would be a very expensive babysitter (half of the mother's income). Why should women accept that?
Btw., I've heard that in custody trials men actually tend to come out quite well. But I think it has to be taken into consideration that fathers probably only go to court when they see a chance to win to begin with (mother is a crack whore or whatever). So that statistic alone is not telling much.
