Damon may not be his responsibility, but in a way he is. The same way that Stefan was Damon's after Klaus made him go with him. They're always going to have some amount of responsibility to each other. That's part of what being family was.

Even one as screwed up as theirs.

"Maybe not. But I'm not sure I want some werewolf turning you into a chewtoy either."

Stefan do not start making dog jokes about Elena's boyfriend. That's not nice.