There’s a pretty big difference between an adult woman, with her fully developed nervous system, her lifetime of efforts and memories, and her social relationships, and a bundle of cells. The woman is already an active participant in the social contract-- she makes her contribution to society, and she has an expectation of her rights to be preserved.
As for “baby,” this is the issue, isn’t it? I’ve seen babies. They have 10 little fingers and toes, fuzzy little heads, and they say “wahhh wahhh” a lot. An early-stage fetus clearly isn’t that. Yes, it has the potential to BECOME that, if fostered. But many thousands or possibly even millions of fertilized eggs are lost each year without the woman’s knowledge-- should we not establish constant checkups to make sure that not a single fertilized egg is lost, ever? Or perhaps, we should sterilize every person, and allow only in-vitro fertilizations, so that we can ensure that every single fertilization is brought to term?