If a woman does not want to support a child, she can choose to have an abortion. Of course, the would-be father ultimately has no say in this decision (he cannot force or prevent an abortion). Presumably, the asymmetry here relates to the fact that pregnancy and childbirth burden the mother to an infinitely greater extent than the father. What I don't understand, though, is why fathers may be forced to support (monetarily) children which they didn't want. If a woman decides to have a child in spite of her partner's disagreement, shouldn't she also assume full responsibility for that child? It seems as though the man has no say at all here. If the man wants the child, the woman may nevertheless abort; if he doesn't want the child (but she does), he nevertheless must support it.

I am not sure what is the philosophical question here. Of course there is no general moral principle that guides the rules that you're evoking and you may imagine a huge cultural variation in different legal systems. There are legal systems which do not recognize the right to abort to a woman who doesn't want to have a child as well as there are legal systems (actually, most of them until recently) that do not oblige a man to support his child if, for example, the child is born outside a legal mariage. The rights of women to decide upon the destiny of their future children seems a very recent contingency of some of the contemporary legal systems, and not an inevitable consequence of the difference between men and women. It is unclear in the question whether you complain of this state of affairs (that probably refers to contemporary United States) or you ask what is the underlying moral principle that justifies it. If it is the second one, I would say that there is no such a principle.