Today, Dennis Prager released an excellent video presenting five non-religious moral arguments against abortion. Please give it a watch. I'd like to focus on the first of Prager's five arguments, which is that even if the unborn are not persons, it doesn't mean, ipso facto, that abortion is moral.
Now, I've argued elsewhere that the unborn certainly count as persons. Being a person is about the kind of thing you are (an individual substance of a rational nature), not about the kinds of things you can do. However, let's look at it the opposite way. What if the unborn really aren't persons?
In a compilation of essays, philosophers Frank Beckwith (pro-life) and Louis Pojman (pro-choice) wrote the following: "Another popular prolife argument goes something like this: Because the unborn entity is a human being from the moment of conception, and because it is morally wrong in almost all circumstances to kill human beings, therefore, abortion in almost all circumstances is morally wrong. Although the prolifer is certainly correct that the unborn entity is a human being in the genetic sense from the moment of conception, it is not clear from the biological facts alone, without philosophical reflection, that the fetus is a human person and possesses the rights that go with such a status." 
Other philosophers argue that the question of personhood is meaningless because all people mean by "person" is "an entity with rights and value," which is exactly what is at stake in the abortion debate. So from this perspective, arguing the unborn are persons is just redundant because the debate is about whether or not the unborn have rights and value. Plus, I am certainly identical to the embryo that was in my mother's womb, even the zygote that was conceived from my mother and father. That biological entity was me, so if I have a right to life now, I had a right to life then. So even if I didn't qualify as a "person," it is by no means certain that I did not have the right to live.
So contra Beckwith and Pojman, two intellectuals I respect, I don't think it's true at all that "it is not clear from the biological facts alone" that a fetus is a human person and has rights. Our forefathers certainly didn't agree with Beckwith and Pojman. In the Declaration of Independence, they wrote that they considered it self-evident that all men are created equal and endowed by their Creator with certain unalienable rights, such as the right to life, liberty, and the pursuit of happiness. A fact that is self-evident is one that is evident even without philosophical reflection. These are human rights because these are rights we all have by virtue of being human, whether or not we are persons. The term "person" has been used in the past to justify all sorts of atrocities. The unborn are just the most recent group of human beings to be denied their basic rights.
So again, while I think it can be argued very persuasively that the unborn are persons too, it ultimately doesn't matter in the abortion debate. What does matter is that the unborn are human beings and all human beings have rights by virtue of their nature as human beings.
 Introduction, from The Abortion Controversy, 2nd Ed., ed. Louis Pojman and Frank J. Beckwith (Wadsworth Publishing Company, 1998), p. xiv.