I think a lot of people fail to realize the circumstances in which this might be an issue. Most people's responses are "the both should have been more responsible" . . . which is a true point. However - a lot of these types of paternity-fights happen with MARRIED couples who fall apart during pregnancy due to one reason or another.
The nature of the relationship and the situation surrounding the pregnancy STRONGLY dictates what can and cannot happen.
If a couple is married and she's pregnant and *then* something happens - they split - he absolutely should have the right to demand she carry that baby if he 100% will take care of the child.
Also the man should not have a legal say because at that point he can not legally prove he is the biological father.
I'm quoting these two posts as they introduce the last and most heinous [art of the unfair position some fathers come into where a mother decides she does not wish to gestate OR keep the baby after birth.
I've already stated my position regarding a father being able to rescind responsibility during gestation if he does not wish to be a father - however what about those fathers who do want the child?
In the US, the father (when he knows the mother does not wish to keep the
born child) has to find and sign his local state "putative father" registry - registering an interest in the unborn child. There may be three consequences of this action
1) the mother agrees to carry to term and hands the child over
2) the mother decides (if she is still "early") to abort either because she doesn't want to carry to term or because she wants to deny him the child.
3) the mother rescinds her wish to abort and could hand the child over to the father (very rare) or keep it herself and then make him pay child support and he might even have to fight through court for contact / access / visitation (whatever it's called in your country)
In the UK, the father has to make sure his name is recorded on the birth certificate ONCE the child is born.
Failure to do either and the mother can still quite easily decide to hand the child over for adoption. The father then has the expense of trying to reverse this through court and many judges still side with mother (if it even gets to court).
So in essence at present, a mother has sole choice over whether to abort, if she decides to continue to gestation she can simply hand over the child to an adoption agency. If the father didn't sign a "putative father register" or make sure his name went on the birth certificate - she gets to take away his parental responsibility too.
In all cases, the laws and procedures are heavily against the father (and child).