Well, yeah. But they’re wrong, so. 
It’s not, though. A baby is a baby, and a fetus is a fetus, and an embryo is an embryo. They’re different things, much like an apple seed and an apple tree are two different items and nobody would confuse one for the other. I suppose the *exact *point at which one becomes the other can be debated and is fuzzy and is a process, as you say.
But then again at the point in time and gestation where the overwhelming majority of women, American or otherwise, undergo an abortion procedure - and certainly those that do so by choice to remain child free rather than because of medical complications emerging later in their pregnancies - we’re well before the point where it even *threatens *to become fuzzy. Since this particular timepoint and the morality/legality of electives are the crux of the debate (because even in God-fearing America only a vanishingly small minority of loonies are of the opinion that “fuck the mother, let her die if you have to so long as babby come out !”), this seems fairly relevant.
**Terr **mentioned kicking. That starts to happen around the tail end of month *four *at the earliest. Abortion’s pretty damn strictly controlled at that point, across the globe, and electives are well into the “are you fucking kidding, lady ?” legal range, both in the US and in my own country. I happen to be very OK with that.
Within the legal abortion-by-choice period, embryos don’t kick because they don’t have legs. Or a nervous system that would send the electrical impulse necessary for a muscle contraction, really. And even if they did kick, their mother wouldn’t feel the kick because they’re about half a centimetre long from head to* tail*. If you ever saw one and didn’t already know what it was you’d think it was some weird, alien larva and feel a pressing urge to kill it with fire. Which is not a typical reaction associated with babies.
So, no, sorry, that’s not “a baby”, and it’s not the mental picture that flickers on when people hear the word “baby”.
It might be a person, which honestly is neither here nor there; it might have a soul though as a staunch materialist I personally doubt that very much; it might be alive, viable, born, have legal rights, whatever you want. But one thing it’s definitely not… is a fucking baby. Words have bloody meanings.
I’m not trying to “win” any argument. I could care less what the abortion laws are in the US.
I was merely trying to explain to **Nars **why the use of the term “baby”, with its positive/emotional connotations, would be problematic rhetorically speaking on top of being inaccurate both medically and semantically speaking.