Many legal arguments rest on fallacies, or at least assumptions, but its still law. I wasn't talking about the logical merits of the argument. I don't agree with the argument.
But first and foremost they're making an ethical argument. And, moreover, the law can and does take circumstances and contingencies into account. For example, in some cases it is already legal (and, in my opinion, perfectly ethical) to kill an alive human being who even possesses personhood, i.e.; active human euthanasia in Oregon. So we need not fear that using personhood rather than life as an ethical criterion will be in any way more problematic, legally speaking, since we may apply whatever contingencies we see fit to the situation at hand.
Edit: I should also add that, far from being a sufficient condition, life is apparently not even a necessary one to establish personhood, as evidenced by the fact that corporations are granted the legal rights of persons.