I do support the basic intuition here, I really do. But there is a crucial difference:

The mother has the right to abort, since it is her body. No one can have say in what happens to her, including the father. Now, if the mother decides to abort, there is no child.

If the mother decides to give birth, there is a child - which has a right to adequate parenthood. This right of the child produces a duty on the side of the parents. And that is the reason the father is forced to care for it.

I really get it. Why should the father have to pay for a child he did not want? It is the mothers decision and thus her responsibility. But this parent centered reasoning disgusts me to be frank.

It is not the parents right to have a child or have freedom from responsibility that is at stake. There is a small, helpless human being which has rights as soon as it is born. And since we have no better solution, the biological parents are assigned as the ones who have the duty to provide adequate parenthood, as long as they are capable. That includes the father.