The idea that the father should have a right to walk away from responsibilities and rights to the child is called financial abortion, I've heard. I support it in theory, but it does have some kinks to work out, such as abortion not being available to every woman, abortion being painful and expensive, children living in poverty, etc. For it to really work, abortion would have to be legal and easy to get everywhere, and affordable.
And of course, he would have to inform the woman of this early on. No skipping town while she's in labor and delivery.
But if this ever happens, it's pretty far off, considering courts have decided male rape victims should pay child support.
This teenager had sex with his teacher, and the woman went to jail for statutory rape. But she was pregnant, and the kid is going to be forced to pay child support after he's 18.
Not to mention
this woman actually kept her boyfriend's condoms without his knowledge, used the semen to get pregnant, and was granted child support.