You are saying a man does not automatically become the legal guardian of a child.
So why does automatically pick up responsibilities.
The right to not have your child given away to the state without your knowledge or consent is hardly a "special" right". It is inherent to be a parent.
He does not automatically pick up responsibilities, why on earth would you think such a silly thing? He only picks up responsibilities if his paternity is established, which is the same point at which he acquires access to all other parental rights.
As has now been told to you several times, both parents have the same ability to use the safe haven law. Equality for all. If such a law is used, neither parent has any responsibilities to the child and it becomes a ward of the state. If the woman has an abortion, no one has any responsibilities as there is no child. If the child is born, both parents have responsibility. In all of these cases both parents have the same duty to the child.
What you want in your piggish misogyny is for men to get an extra special right to abandon a child after it is born and leave the other parent to shoulder the burden alone. There is no corresponding case for women in that way at all. I love it when self described conservatives whine and shriek about how they need to be given extra special rights that no one else has because they're so picked on.