Key here is "outside of the mother's body". Plenty of babies are cared for by people other than their biological mother, I'm sure you've heard of that.

What I am sayin here is that if there was a process by which we could take an unwanted fetus and implant it into someone else / allow that child to exist outside of the physical body of a person that doesn't want it, then sure, that is possibly a better alternative to abortion. Short of that, people should not be forcing other people to give births against their will.