Why do Miles and Winnie disagree about death and killing?

Winnie and Miles have completely different perspectives on life because Winnie is mortal while Miles is immortal. Winnie therefore has a much greater respect for the value of life. Miles, on the other hand, has no sense of just how fragile, how precious life can be; his immortality blinds him to the quality of life. We see this in how he treats animals, for example. Winnie becomes rather upset when Miles catches a fish; to her, it's very cruel to treat animals that way. As Winnie is mortal, the very thought of death makes her deeply uncomfortable. But Miles' immortality means that death is utterly meaningless to him. For him, death is just an inevitable part of the endless cycle of life. Without death there can be no life. Winnie herself comes to develop a similar understanding over the course of the book.