If the man has no rights over whether the child is born, then he should have no responsibilities at all towards the child either.
There was a scene in the movie "The Time Traveler's Wife" where the guy decides to have a vasectomy because he couldn't deal with his wife's miscarriages. The wife in the movie treats it as an unforgivable offense against her rights. I couldn't help thinking, that if the script had had her deciding to be sterilized, women would have been outraged of the guy had objected to her exercising her reproductive choice.
If the man has no rights over whether the child is born, then he should have no responsibilities at all towards the child either.
I absolutely agree.