It's not so. I am staunchly pro-choice. I happen to like babies a lot. They're cute. Mine were adorable and are growing up to be awesome people. I also happened to mostly enjoy my pregnancies, although I grew to miss my ankles after a time.
I also never, ever want to be pregnant, or have babies again. Ever again. I don't think anyone who doesn't want to carry a pregnancy should be forced to whether by legislation or by circumstance and lack of resource.
The confusion of the anti-choicers seems to stem from the insistence of Ms. Clinton, along with grandparents-to-be Bill and Hil, in referring to her impending offspring as a baby.
Part of choice involves the decision to imbue meaning on a pregnancy. I'm reminded of the passage from The Little Prince, where the fox explains if the prince were to tame him, to establish ties with him, that to him, the fox would "be unique in all the world" and vice versa.
In a sense, a person who is carrying a wanted pregnancy has established ties to the fetus, has began thinking of it as a baby. The pregnant person has made a choice (whoa, there's that word again) to establish ties with what is growing inside. In the story, the Prince does decide to tame the fox, although in the beginning, he has misgivings about having much to see and places to visit. He makes the choice to tame the fox anyway, and the fox says to the prince that "You become responsible, forever, for what you have tamed."
That's a big deal and a choice that should not be foisted on someone. But more, it's a decision made by a pregnant person, followed by their partner and eventually their friends and family, to establish those ties. So, it is not hypocritical for a pro-choice person to refer to a wanted pregnancy as a baby as opposed to a fetus, once they have made the choice to establish that tie, to give it such meaning.