When I teach abortion in my ethics class, I am often suprised how many students are pro-life. But this should not surprise me, and I think pro-choice people are to blame in part for how the debate is framed.
The fact is that abortion is a serious moral issue. If you think that an ordinary human being has intrinsic value, then there is a prima facie case that abortion is wrong. I don't think this argument really persuasive, but it is a mistake to ignore it.
Here is a better strategy, in my view. Abortion is a serious issue. It may be immoral in some cases. But its not obviously immoral in all cases, even if we add the typical exceptions of rape, incest, and life of the mother (why is "incest" different from rape, if we are talking about children?)
We need to distinguish (1) is abortion wrong and (2) is it the right thing to make abortion illegal.
This is all obvious, and almost anyone who has thought about the issue draws these distinctions. But in the debate, the issue is simply ignored. You have pro-life people asserting, as if it were not a matter of interpretation, that abortion is "murder," and you have pro-choice people arguing about a woman's right over her body. The latter argument fails to engage since it makes it look like pro-choice people are just oblivious to the fact that biologically, you can have the precisely same entity in and out of the womb.
A better strategy is to say up front: this is hard a issue. Who knows when a person comes into existence. Who knows when it may be legitimate to end a pregnancy. Whatever is true, abortion is not like blowing up an orphage or randomly shooting six month old babies crawling around your living room.
The issue is just too complex for a law to decide for each woman in each situation. When put this way, abortion as a woman's rights issue makes a lot more sense. Its not that there is an obvious answer to the moral question, but that precisely because there is no such obvious answer, its best to leave the decision to the individual and keep the government out of it.