i know it might seem random but i have this senario in my head where damon can start to look after carloine like giveing her vervain so she won't be compalled now that an origanel is in twon and compall vampires, and then they would start talking about her dad and he might someday come back and kill her and damon tells her about how his father killed him & stefan when they were humans only because they tried to help a vampire and since caroline's dad is 100% vampire hater he might do the same and damon asks her what she would do if it comes down to her or her father (i mean if her father might try to kill her,would she ket him kill her or will she kill him first) at that moment damon offers to kill her father (do the dirty work) so she wouldn't have too, and maybe she will see that damon always had to the dirty work to keep elen safe

Damon was a very good friend of her in season 2. Okay, he wanted to kill her, but he couldn't do it because of Elena. After that they became good friends. Damon cared about he whe he said Caroline doesn't be a friend of Tyler and he saved her in 2x20 and she saved him (and Stefan) in 2x05.