I think you mix several things. When people say "my body, my choice" is because pregnancy happens in a woman's body. Pro-phoetus usually "forget" this detail. The fact that the phoetus develop inside a body that goes through changes like displacing organs needed to live, atropiate those organs, feeds directly from the woman's blood, might even kill her if it is in the wrong position or develops wrong... All that is conveniently ignored and not talked about.

That is why while the pregnancy happens, choice is up to the woman. Because it happens in her body, not on the male body. She'll be the one who endures either an abourtion or a pregnancy and a birth (which is very painful even with sedatives).

In the hipotetical case she doesn't abort, and a child is born, then both parents have obligation to the baby. Because once born is no longer a phoetus the same way that a some point a baby becomes a toddler. Then, both parents can give it for adoption. But if one refuses, the other would pay child support. You complain because it is rare that it is the father the one who wants to keep it. I get it. You would like that men decide if the woman continues pregnancy or, if they don't want it, to just say "do what you want but I'm out". Except the health at risk is the woman's. And once a child is born, the one who has rights is the child.

I'm guessing the solution could come by taxes and benefits. In countries or societies where people is willing to pay higher taxes so single mothers won't have money problems to raise children on their own, then man could just say "I don't want to be a father". But right now it would be complicated.

For now, until an artificial womb is developed so a woman who doesn't want to remain pregnant can just put the cygote or the phoetus there, forcing women to continue a pregnancy (that could kill them or left them with health problems for life) is wrong.