Why did they want to kill the woman?
I haven't seen the movie, but from what I can understand, the young woman became paralyzed and was in pain so she didn't want to live. The story line is supposed to be about the Eastwood character taking the responsiblility to carry out the girl's wish to die, regardless of the moral guidance of a priest. In other words, the Eastwood character makes a conscious decision to disregard the religious advice of the priest. And, that's supposed to be a good thing in the movie.