But it wasn't a deep experience with a girl. It may have been a deep experience for you in the depths of obsession, but the girl had nothing to do with it. You were infatuated with an idea of her, which is something very different from loving her as an autonomous agent who chose to journey through this experience with you.

and I have the trouble to grasp the full lesson out of.

The lesson is not to obsess over people. Plain and simple.

Why would you be nice to someone, who is in love with you, if you don't want him?

Because she was nice.

I had really trouble communicating with girls afterwards.

Yeah, it seems like your inability to process this and move on has profoundly stunted development of interpersonal skills, particularly with women. I think it'd probably be best to visit a therapist in order to get back on track in a timely manner.