As [MENTION=1206]cascadeco[/MENTION] mentioned, once feelings have developed, they don't exactly just go away. Rejection really stings, and people have a habit of holding out hope for love where reason would have given up much earlier. The pattern shifts quickly from a healthy one based on mutual respect and esteem, to one of dysfunction and codependency.
Certainly, if he's sticking around, he likes the girl and wants her to like him back, and that this would make him feel better about himself. Instead, he should concentrate on improving himself, and if she's attracted to him, she'll let him know somehow. Furthermore, if he wants to be a friend, this is how one goes about being a better friend to others.
Exactly the opposite. It requires not thinking so damn much. It requires being comfortable enough in your own skin to just be.