Well, I'm not American but there are two différents things to take into account: Before birth, only the wellbeing of the parents is important. After birth, there is a third human in the equation, therefore the wellbeing of the kid also must be taken into account.

This directly correlated for part 1 to abortion rights, while the 2nd part correlate to the need to decently raise the kid. In most part of civilized world, we do have social security nets and financial help for single parents. Therefore, the father abandoning the kid is "not that big" of a problem, and we can let the father choose to do whatever he want. Problem with America is that these social safety nets don't exist or at least are clearly insufficient. Therefore, to protect the kid's interests, you have to force the father to provide for him. That's another nasty effect of a country which do not invest enough in its population's wellbeing.

TL;Dr; I'm pro-choice AND pro-father-choice, but only in developed countries where the kid can be raised decently without father's income, which excludes USA.