Who was it that down played the role of the father in all this?
You are conflating (intentionally, I suspect) two different things here: the mechanics of creating a child versus the act of raising a child once it is born. The burden on fathers for the former is virtually nothing. The burden on the man for the latter (we agree, I believe) should be shared. Given that, I don't think it is a difficult leap of logic to conclude that the woman gets the legal right to make decisions WRT the former and the man should share responsibility for the latter.
Taking your position means the women get to have their cake and eat it too. If the baby is half the father's right after birth then by God it is half his prior to birth. My point is extremely relevant to the situation. There are downstream ramifications to society telling young men they are short time players in the process. No wonder so many say "screw it" and walk away.
Not a single man in the history of ever said "screw it" and walked away because he was told that his role in the in utero gestation of a fetus is negligible. Every man who has ever had a child has been patently aware of that fact. It is the very fact that a man can create a child with so little personal sacrifice that makes it so easy for so many men to walk away. A woman cannot walk away. SHE has to deal with it in some way. She has no other choice. A man can hop on the next bus out of town and never see mother or child again.
So if you're mad that so many men do walk away, blame God for not making us go through the morning sickness, the pain, the health risks, the labor, the inability to carry on with normal life ... not dirty libruls. Ancient cavemen realized that they didn't have to do chit to create their children either, way before Gloria Steinem came along ...