Do you acquire the rights associated with personhood or are they essential to you? Consider rights in general, the right to vote, for example. You didn't always have this right. You acquired it. So, perhaps personhood is like the right to vote. You acquired it at some point in your development.
The right to life goes along with being a person. If you are a person, anyone who kills you has committed a moral and legal wrong. Most pro-choice arguments talk about this right as if it is acquired at some point in the womb. Prior to counting as a person, however, it is morally justified to kill the entity in the womb.
Personhood, however, is not like the right to vote. A right to do some thing or have some social standing is parasitic on the more basic question of what kinds of things are things that can have those kinds of rights. The most obvious answer is that persons have rights. But if so, then the kind of thing you are is a person and it is in virtue of you being the kind of thing you are--a person--that you can acquire all sorts of other rights (the right to vote, for example). But notice: being a kind of thing is not something acquired; it is something you are. Nothing of any kind acquires the property of being of that kind. If so, then you always were what kind of thing you are now - a person. There was no point after your conception that you changed from one kind of thing into another kind of thing. Therefore, it is wrong to kill the person in the womb at any stage in its development.
John Feinberg and Paul Feinberg, Ethics for a Brave New World (Wheaton: Crossway, 2010), 102.