Thanks to everyone for their contributions, and especially to Bette for reminding us of the importance of hearing women's voices on such topics. I'll add one more point, along the same lines.
The questioner says that, if a fetus has a right to life, then abortion is immoral and should not be permitted; if not, then it isn't immoral and should. But surely this is wrong. I have a right to free speech, but it does not mean that I have the right to cry "Fire!" in a crowded theater. Other people have rights, too, and their rights can sometimes out-weigh mine.
The same is true in the case of abortion. The mere fact that the fetus has a right to life is compatible with a pregnant woman's having other rights that might out-weigh the fetus's right to life in some cases. For example, the woman herself has a right to life, and I for one have a very hard time seeing why that right should not trump the fetus's similar right if the pregnancy is endangering the women's life. Similarly, a woman has a right not to be made pregnant against her will, and it is the central point of Judith Jarvis Thomson's classic paper "A Defense of Abortion" that, when that right is violated, then, even if the fetus brought thus into being does have a right to life, even one as strong as that of the mother's (a claim Thomson concedes for the sake of argument), that fact does not make aborting that fetus impermissible. Thomson's argument for this claim has always struck me as absolutely compelling. But if so, then abortion is morally permissible at least when the life of the mother is threatened or in cases of rape, and that means that the mere fact that a fetus has a right to life does not make abortion morally impermissible.
That said, if the fetus does have a right to life, that might well imply that abortion, even in cases where it is morally permissible, nonetheless has moral costs or is morally regrettable. And, as Thomas Pogge has so ably argued above, there is nothing unusual about that.
The difficult question is what rights women have in this regard, and how those rights interact with whatever rights the fetus has. Are there other cases in which a woman's rights might outweigh the fetus's? Are unintended pregnancies such a case? Does it matter if the woman and her partner were responsibly using birth control, which failed (as sometimes happens), or were being irresponsible and simply ignoring the possibility of pregnancy? These are all good questions, even if, as I'd be inclined to argue, abortion's being morally impermissible in some such cases does not imply that it ought to be illegal. (I really do not want courts trying to make such fine distinctions under severe time pressures.)
But we can't even have this kind of discussion until we recognize that simply saying "The fetus has a right to life!" doesn't end it. It only begins it, because the women carrying these fetuses have rights of their own. It is because so-called "pro-life" advocates flatly refuse to recognize this fact that they continue to be vulnerable to the charge of sexism and, frankly, to have no decent response to that charge.
All of that said, I'll close by expressing what I think is agreement with Bette. I often find myself unsure whether the language of rights is really appropriate to the evaluation of such a profoundly personal decision. Might it not in some cases be a loving though still fraught decision to choose not to bring a child into the world, made in the full light of consideration of that child's prospects for health and happiness, even once his or her development has begun? A difficult, even heart-breaking, decision that a mother makes on behalf of her child, just as parents often are called upon to make hard decisions on behalf of their children? I have heard women describe their choices in terms not unlike those, but only rarely does one hear anything along those lines in our public conversation. Why not? Because women's experience is excluded from that conversation. That's why.
Try this account, written by a woman who got pregnant because of rape, if you want to start listening to the unheard.