We're talking about people who want abortions, so yeah... Most people who want abortions have unwanted pregnancies. Your assumption that the majority of parents will just "step up" is based on what exactly?
If a woman in your world has to take care of every baby she gets pregnant with, why wouldn't it be fair that every man has to as well? You suddenly think it'll infringe upon the man's freedom? But it's okay to infringe on women's rights? Women have the right to freedom too.