They're ready to admit that there's no real difference between babies and fetuses now because they think they can win the debate on killing babies.
The whole trick depends on the shift from "it is wrong to kill an innocent human being" to "it is wrong to kill an innocent person." We can say without any scientific doubt whatsoever that a baby is a human being, and by nearly any ethical standard it is an innocent one. But is it a person? Well, now we can play with words!
Beware, of course, who else gets defined out of "personhood." But more than that, we should just refuse to make the shift. We don't need the ambiguous category given that we have the obvious and clear one. Humanity is easy to establish. The whole appeal of "personhood" is that it isn't, and thus can allow for immoral acts to be slid in where convenient.