My wife and I are expecting our first child and one of the things people have asked is what we will do if our cat (she's an adopted rescue) and the baby don't get along. With a straight face I tell them that the cat was here first so the baby will be put up for adoption. That usually gets a shocked response.
My wife and I agree that we would not send the cat to a shelter or to live with someone else. She's part of the family and we'll find a way to make it work (if it becomes a problem). The problem is that people look at their pets as just animals when in fact they are truly a part of the family.
It's really just sad.