Not so. Custody can be (and is) enforced by the court, for example. So when you say ‘only,’ you really mean ‘just one.’
That is the most illogical statement you've made so far - and that is saying a lot. If the man doesn't want to maintain a relatinship with the child or pay child support, I don't think he will be suing for custody, so your statement has no relevance to the discussion at hand.
You keep dodging the issue. The point here is that no law is going to force a man to maintain a paternal relationship with a child not his own. The only thing it can do is force him to pay for another man's child against his will.