Why couldn't the annoying dog get on Papyrus's nerves?
HE'S A SKELETON. HE DOESN'T HAVE ANY.
Listen here, bud. You see, Papyrus is a skeleton. Skeletons don't have nerves. So the dog can't get on his nerves because he doesn't have any! Get it? You are probably so unhealthy that you would die if you ran a mile.