Some people think that the fact that people cannot agree about the issue of abortion is good evidence that moral values are relative or subjective. It is quite true that there are profound differences about moral values that are extraordinarily difficult to resolve when it comes to this issue. It is also true that a lot of the dispute on this issue takes place at what I call the bumper sticker level: "Abortion is murder" "A woman has the right to do as she pleases with her own body," etc.
However, disputants do agree that humans in general have a right to life. No one, (or almost no one) disputes that. There is a very strong consensus about the right to life outside the womb, even amongst pro-choicers, which is challenged in some cases by Australian philosophers taking pro-choice arguments so far as to justify infanticide, but by and large social consensus against infanticide is pretty strong. No one thinks we have the right to knock off a four-year-old just because the four-year-old is annoying us. People also believe in the right of persons, including women to control their own body. Pro-lifers are not inclined to oppose that right except in the case of a pregnancy, where they believe another person's rights to be involved. Pro-lifers and pro-choicers also agree that the quality of life matters a great deal. It is just that pro-lifers think that quality of life concerns have to be set aside in order to protect the right to life of the fetus, the exact argument that a pro-choice person would make on behalf of four-year-olds.
Hence the contemporary debate concerning abortion is a kind of in-house quarrel between people who agree on a range of fundamental principles. Looked at in this way, the dispute about abortion provides an problem for moral subjectivity, not an argument for it.