A woman is in the hospital for complications with her pregnancy. The doctor tells her that if she gives birth to this baby, she will die. So the woman has two choices. She can kill her baby and live or she can give birth and die.
What does she do?
The scenario you mention is just one of the imaginative scenarios brought out in the late 60's to justify abortion.
It was used as a foot in the door, (by persons pretending they ONLY wanted to save women's lives), for abortion-on-demand (ie, killing a human for convenience).
How about this scenario--a baby is being born, breech. Her father is in the service overseas for the past 3 months. She is just beginning to emerge from the womb. The "still-legally-pregnant" woman doesn't realize, until that moment, that the female fetus is "racially mixed." The woman was sure she had taken adequate precautions, during a one night stand, nine months before. Her husband will know the child is not his.
Should the doctor follow the woman's directive and perform a partial birth abortion so the husband will not realize his wife had an affair?