The most common argument for the Pro-Life side of the Abortion Debate is that life begins at conception. In this model, the insemination of the egg is what triggers the process that creates "life" or "personhood" in a fetus. While this is not scientifically proven as of yet, it is a reasonable argument because the fertilized egg will, in a healthy adult, grow to term and produce a baby in most cases. If one argues that a non-terminated fertilized egg will almost always produce a baby -- thus producing a "person" with all the rights of other humans -- then it is logical to state that the fertilized egg is as deserving of rights as the birthed baby.
This model would also cause the attending doctor to be vulnerable to charges of murder; aside from the still-unresolved Hippocratic Oath issue (non-legally-binding), if one terminates a growing life that is deserving of rights, it is the same as terminating an already-born life. Current debates over how long into term a fetus can be aborted are attempting to redefine "life" and giving rise to the unsettling notion that a baby could be carried to term, birthed, and then aborted; most pro-choice advocates claim that this extreme will never come.