An egg does not have the power in and of itself to become a baby. Given its normal development, it will die just as it began, an egg. A fertilized egg, however, is no longer an egg. What is it? Science shows that it is a member of the human species, not the mother, not the father, but unique unto itself. Given its normal development, it will eventually become an adult.
The input given the blastocyst is nutrition. Its entire developmental process is initiated from within and not from without. The mother, while providing the correct living conditions for the blastocyst to continue to develop, does not start the process nor control the process. It is self-initiated.
The fertilized egg is not a part of the mother's body. Therefore, she has no right to choose. To say she does is to say she has the right to choose to end its life moments before birth, immediately after birth, or any other time, for that matter, because there is no difference other than those differences I stated before.
Whether life begins at conception is the crux of the issue. If so, you are intentionally ending the life of another human being by having an abortion, regardless how easy it is to do, how little attachment you might seem to think you have to it, how much it doesn't yet have arms, legs, and a face, how difficult your life will be because of it, how acceptable by our current society, etc. Any other discussion is really pointless.