There are only two ways there can be disagreement at this point;
1) Mother wants baby/Father doesn't
2) Father wants baby/Mother doesn't
To me it's common sense that the parent who wants the child should agree to be financially responsible for the child and if the other parent forcibly terminates the pregnancy punishment should ensue.
Right, but I am playing devil's advocate here.
In option 1, the father does not suffer any additional physical harm, and he can terminate his rights. We are also arguing in this thread that he should not be automatically forced to be financially responsible for the child. I can think of some scenarios where the mother might sue for some sort of compensation, but those are going to be the exception and can be handled in civil courts as a contract matter.
In option 2, however, the mother does suffer additional physical harm. She terminates her rights after birth. She should not be automatically forced to be financially responsible for the child, either. How do you force someone to continue a pregnancy, alter their body, put their life in danger, disrupt their life and work habits, etc., for a child they do not even want? How do you force them to be healthy? How do you safeguard a child who is held hostage for months and months by someone who does not really want them to live? It can all be handled privately, but I keep seeing courts and force batted around. The issue of physical changes and risks does not seem to be addressed, and like it or not it is gender-dependent. The only real way around it is putting a price on pregnancy and labor and delivery, and I'm not sure that does anyone any favors, either.
Option 2 relies entirely on using someone's body against their own consent, with significant risk. Option 1 relies entirely on using someone's own body with their own consent, with the risk only assumed by the person who wants the baby. That's why it's relevant who is carrying the baby.
This could go even further, by the way. Babies benefit greatly from breast milk from a healthy mother. Is there a right, then, to extract milk from the mother before the father takes custody? Must she be available for that? Don't be too quick to dismiss this.
Ideally it should be handled by knowing your partner up front, but after the fact, I don't think we benefit from bringing the law into it. All the questions above have to be answered by the parties involved, not by government. It used to be that a family might gather together to raise a little "accident," or perhaps the gal in question was shunned a bit. I think we are approaching the time when the guy is also frowned upon for his Johnny Appleseed ways. That should be enough, without the overpowered hand of the State getting involved in something so personal and intimate.