I believe that the fact that abortion is 'out there' frees men from taking responsibility.
Abortion is the act of a woman killing a couple's child. That is a crime against men. It doesn't "free" men, it takes the children of men from them by deadly force.
Even if his girlfriend chooses to have the baby, a father can justify avoiding responsibility because he will tell himself, "I wanted her to have an abortion, she chose not to," or whatever lets him sleep at night.
Look at your own language. The sole sphere of existence that you align with fatherhood is responsibility. You do not mention his rights at all. Again, a bitterly cold view of fatherhood.
I’ve read cases on FR of men who did NOT want their child aborted but the woman did anyway, and cases of men practically dragging the woman they impregnated into the abortuary even against her will.
Both men and women need to be responsible for their offspring and they can start by having sex within marriage. That’s a huge first step.
The reality is that men are pressuring their girls to have an abortion they don't want. I know of one young teenager who was pressured by her older boyfriend into doing just that. Of course she bears some responsibility, but if the guy would have wanted to get married, she would have kept the baby. You can talk about what happens in theory, but the reality is that most girls are pressured by their boyfriends into an abortion that they don't want, usually by threatening to break up. That is what is happening. Go to an abortion clinic and see for yourself.
There are good men who want to claim their child and the mother wants to have the baby. For them, abortion is not an option. Taking away abortion wouldn't affect them.
There are also good men who want their baby, but the mother wants to abort. Taking away abortion would actually help these men keep their baby.
There are also bad men who do not want to take responsibility and want to kill their child. Take abortion out of the picture and the mother is not pressured to abort, because it does not exist.
Finally, there are couples where both the man and the woman don't want the baby. This is the trouble spot, or would be if there weren't so many couples wanting to adopt. So, removing abortion is a good thing in this case, too.
I think that making abortion illegal actually increases the rights of men, as well as the responsibilities.