I think it has been a part of zombie folklore since the original Night of the Living Dead to play off the scenario or your loved ones being the thing you should fear. It's easy for us to watch it in movies or television and say, "Sure, I'd kill off my sister/brother if they were bit". But in reality I don't think many people could.
I fully admit that I could not "deal with" my familiy if they were bit. I'd have to let someone else do it because I just do not have it in me. That said, I think it would be considerably easier to kill off random zombies whom you had no prior relationship with.
I think many of us survivors would have our own barn to deal with our family.