Stefan Did That on Purpose
He intentionally antagonized Caroline so she'd give her engagement ring back to him. Bet that he did that because he wanted something to "anchor" him to not lose control again and be a little closer to his humanity.
It was noted in the episode (by Stefan) that Elena's necklace was keeping Damon from completely giving over to being without his humanity. In the beginning, Stefan was trying to not lose control by "wiping the blood away" from his victims. Since when has Stefan cared about not losing control with his humanity off? He hasn't, not until he really had something to lose (Caroline).
The hospital scene was his breaking point, so he decided to push Caroline to giving over her ring so he'd have something to hold onto to keep him in check (notice how he kept it and didn't just toss it).
Thoughts?
Don't be thinking about me when I'm gone.
I wasn't thinking about you when you were here.