(This is an abstract view that doesn't get talked about much by "activists" but some of them do mention it.)
This is because substances might be mental substances, or mind+body substances, or even "soul"+body substances.
One needn't think mere bodies are of this "substance." And so on need not agree that embryos and beginning fetuses are persons, even on this theory of personhood!
This theory can also help respond to "pro-life" reflective advocates of cruelty to animals: if they think that "being a conscious, sentient being that exists over time [that is, doesn't have a mere moment-to-moment existence]" is a poor theory of personhood since it suggests that many animals are persons (and so wrong to kill and eat for the fun of it), this theory can explain why newborn human babies are persons but with no implications for animals.
In general, all "metaphysical" sounding anti-abortion claims can be accepted by pro-choice folks, but with different metaphysics, all of which deny that we are our bodies, or that we are identical to our bodies.
P.S. This can all be stated with "kind" language: what "kind" of beings are we? What "kinds" of beings are rational beings? In denying that a mere body is the relevant "kind" of being, one can propose that we are of the kind "mental substance," or "mind+body substances," or even '"soul"+body' substances. So pro-choice folks can accept and use this type of metaphysical-sounding language too.
@nathan.nobis On the "substance" view of persons & abortion. #abortion #persons #personhood #prochoice #prolife #ethics #philosophy #metaphysics #bioethics ♬ original sound - Philosophy 101 - Prof. Nobis