The principle here is that individuals in our society do not have an obligation to give of their bodily resources to help others survive, especially when they bear no responsibility whatsoever for the predicament of the person in trouble. This principle has been pretty consistently applied and respected in American law and tradition. It's the reason there is no forced organ or blood donation and women aren't forced to carry unused lab embryos to term.
In the case of a rape pregnancy, it seems to me that the victimized woman seeking an abortion has a very strong case. She had nothing at all to do with the creation of the embryo she now carries, so shouldn't this principle apply to her? Isn't she justified in seeking to end the violation of her rights? The only way for her to cease the use of her body by the embryo is to have an abortion. The innocence of the baby is not relevant in this scenario, just as the innocence of unused embryos is not relevant to their situation.
“She had nothing at all to do with the creation of the embryo she now carries, so shouldn’t this principle apply to her? Isn’t she justified in seeking to end the violation of her rights? The only way for her to cease the use of her body by the embryo is to have an abortion.”
Yes, and that is the crux of the matter, that the only way she can hope to assert that right is to kill the baby. Her free exercise of her rights is in direct opposition to the child’s free exercise of his rights. That’s why it is not sufficient to simply assert that she has a right. Yes, she has a right, insomuch as that right doesn’t infringe on anyone else’s rights.
Since they are in conflict, it’s not a clear cut case, and a compromise must be made, to accomodate the rights of both parties, or a subordination must be made if there is no compromise possible. In this case, there is no compromise possible, since the child cannot live unless the mother is restricted from exercising unfettered rights over her own body. One or the other party’s rights must be judged to take precedence over the other.
That’s where the argument for the mother’s rights breaks down. In almost every circumstance, the harm caused to the mother by giving precedence to the rights of the child is vastly inferior to the harm caused to the child by giving precedence to the mother. Only in the circumstance where the mother’s own life is being threatened by having her rights subordinated can one make a reasonable argument that giving her precedence is the correct judgement.