Political disputes about abortion usually involve repetitions of bad arguments, empty slogans, and upsetting images. The assumption seems to be that reason is irrelevant and the important thing is to motivate those who are already convinced. It is as if everyone has accepted the theory that moral reasoning is post-hoc rationalization and that moral disputes in are intellectually no different from sports events in which fans cheer for one side or the other.
Here is a very brief summary of the argument for abortion, drawing heavily on the work of Peter Singer (especially in "Practical ethics"). The point is that reasoning is relevant. (I discuss relevant issues at greater length elsewhere, particularly here.)
Abortion is indeed killing, but that does not settle the issue. Nor does it settle the issue to say that the fetus is "human", since this still begs the question of when and why it is wrong to kill a human. The following reasons come to mind:
First, killing a fetus is a harm to the parents if the fetus is wanted. This is an issue only if the abortion is disputed by (for example) the father. Usually this is not an issue, and is surely not the issue that riles the anti-abortion movement. When relevant, it is a family dispute.
Second, the means of death can be painful. This is possibly an issue for late-term abortions, when the pain system is developed. The solution would be anesthesia for the fetus. The same argument would apply to the killing of animals. This too seems beside the point most of the time.
Third, abortion prevents a stream of future experiences for the person who would be born. On balance these experiences will probably be positive, relative to not having them at all. This argument applies to animals as well as people. It applies to any choice that prevents a person (or animal) from existing, not just abortion but also birth control and abstinence from sex. Carried to the limit, it would amount to a command to "be fruitful and multiply", until we reach the point where the world is so crowded that the totality of negative experiences resulting from an additional person was as great as the totality of positive ones. (Derek Parfit discusses this issue at length in "Reasons and persons".)
Although this argument is interesting, I do not see why we should accept it. If we go one step back and ask why experiences are valued, we find that they are valued because people want them. That is, people have goals or wants for having good experiences (and, presumably, so do animals). So, when we create a person, we are in essence creating goals (or wants) and then satisfying them. But, if the goals do not yet exist, why is it a requirement of morality or rationality to create them just so that they could be satisfied.
For example, why are you obliged to inculcate in me a taste for contemporary pop music? Even if it is true that, once I had the goal of listing to pop music, I would get positive experiences from listing to such music, it is possible that I do not want that goal. It might be inconsistent with my other goals. The Golden Rule thus implies that you have no particular obligation to create goals in me, because I may not want those goals. Nor is it necessarily rational for me to create such a goal or taste in myself. Whether I should do this depends on my other goals.
We have no moral obligation to create beings just so that we can satisfy the goals that come into existence. The Golden Rule does not apply here because the "others" in "do unto others" do not exist. It is the goals of those who exist that determine whether it is rational or moral to create new goals.
A final issue is potential. It is true that a fetus is a potential adult human. So is every sperm-egg pair, and it is hard to see why their physical joining together is relevant to the argument concerning potential. It is just a salient step in the pathway. But the argument from potential raises the same questions as argument from experience. It is not clear why it is moral or rational to create new people and new goals, if doing so is inconsistent with our current goals.
Some of our current goals, in fact, may imply that limiting births is a good thing. We want humans to have good lives once they come to exist. They have goals and wants then. (Of course, we also want enough of them to insure the long-term survival of humanity, but, arguably, long-term survival is more likely if the rate of population growth is slower than it is now.) We want particular children to have good lives. If we are going to limit family size, then we want to time the bearing of children so that they will be maximally wanted when they arrive, and maximally likely to develop well.
If this sounds like an argument for "abortion as a method of birth control", it is. But it does not imply that abortion is just as good as any other method of birth control. Clearly abortion has many disadvantages, including emotional effects. But these do not make it worse than no birth control at all. And often, as in the case of fetuses with serious genetic impairments, pregnancy complications, or failure of other methods, abortion is not the method of choice, but a fall-back.