What do you think this "Why not you?" is short for? "Why can't you be yourself" or something?
ex)David is a handicapped son
--- Only once has David said, "Why me? Why was I born like this?" It was when he was about twenty one, and he asked Ben, his father and my husband, that. And Ben said firmly "Why not you?" It wasn't easy for a parent with a disabled son to respond like that, but he knew that 's what he had to say....
It means "why shouldn't it have happened to you?" (being born handicapped)
It wasn't easy for the parent to say, but it was for the son's good, to put an end to the self-pity.
By asking "why not you?" he is asking why the son feels that he should be so special as to be spared.