Just to be clear, they are worried about what that human being decides to do with the fetus' body.

In a way that does bear some analogy to how one might worry about what a person might do to their child's body.

No it is not an exact analogy, but (to me) it is not unthinkable for someone to ascribe rights to a fetus. And if one does that, well things get sticky huh?

What responsibility does the state have for the well being of a child? of a fetus? who is in the position to dictate the correct morality here? Not me. But then who?

(Note: I am not pro-life, but I can see where such a person is coming from.)