As President Nelson explained:
Another concern applies to pregnancies resulting from rape or incest. This tragedy is compounded because an innocent woman’s freedom of choice was denied. In these circumstances, abortion is sometimes considered advisable to preserve the physical and mental health of the mother.
Because the woman’s freedom of choice was denied, it intuitively feels wrong to require her to bear the consequences of something that was thrust upon her. The case of a rape most closely resembles the famous hypothetical of the “violinist” where a woman wakes up attached to a famous violinist who will die if the woman unplugs from him.