To make themselves feel superior.
Nothing puts this in perspective more than ACTUALLY rescuing an animal. I had occasion to do so once, for a baby kitty who was being abused. No plans to do such a thing, it just happened.
I came by a cat that way once many years ago. Actually, it was my son — about 8 at the time — who did the rescuing.
I have never owned a cat or a dog that was not from a shelter, except for that cat and a dog that I acquired while I was in college because the owner wanted to find him another home.