An infant’s right to life isn’t a normal situation. It exists solely at the discression of its host (ie the mother). Its very existance is dependent on her. If she chooses not to have sex, if she chooses not to be pregnant, that child never “is.” And so, that child’s rights are limited to the extent that the mother grants. If she wants it to live, it has rights, if she doesn’t it won’t.
This is why we end up with the strange cases of murder charges when someone causes a woman to loser her pregnancy. I don’t have the right to take that child, or kill it, against her wishes. Until birth, that fetus is an extension of the mother. Its rights are an extension of her’s. She has the right to life, which means you can’t kill her. And if you do, you will also kill the fetus, and thus be liable for the death of two. No one has rights over that child except the mother. We can’t force her to take prenatal vitamins, go on bed rest, or stop smoking crack.
As long as it is inside her and dependent on her, she is in control. That includes the moment sperm enters her body, right up until that umbilical cord is cut. Potential life, the possibility of being human, doesn’t not trump the rights of an actual living person.
Your throught experiment fails when you realize that if you start from birth and work backwords, you’ll be forced to keep going, to the moments before implantation, before conception, before intercourse, in fact you’ll be forced to go all the way to the point where her mitosis in her ovaries changed to miosis and began producing oocyctes. You’ll need to ask if at that point a woman is still in control over her body and reproductive system. That point when cells start dividing is just as relavant as the seconds before birth.
So here is a better thought experiment. After the baby is born, doctors find that is has a rare form of cancer that only the mother’s blood and cure. I saw this on House so I know it’s real.
Is the mother still in control of her body? Can she decide to let the infant die? Or should we as a society be very, very, very, very, very, very, very, very, careful deciding if she can be trusted to make the right choice? I heard of a woman in China that didn’t make the right choice.