Most Helpful Guy
I think he might still be conflicted about his feelings, or maybe he just wants to be friends? Maybe he's hoping to have a, how should i put it? A physical relationship with you?
You could just outright ask him, he might give you a straight answer..
Most Helpful Girl
1) they're genuinely not over you (this is rare, but it depends entirely upon how you broke up).
2) they want to remain friends with you (slightly more common).
3) they want to use you for their own physical or emotional pleasure (again, depends on the dynamics of the relationship you shared together) - maybe they want you around for when they begin to feel lonely, maybe they know they can use you to boost their own self-esteem. (This can be common after a break up).
4) they are regretting their decision to break up with you or are having second thoughts (again, this is common... but the guy will make it clear soon that he's regretting it. If he doesn't show signs of regret then you can disregard this point.