I think your friend might be on to something---but the word obsession is incorrectly used.

Maybe "geninely concerned", "primarily concerned", would be better to describe what we really feel, when we really love another person.

Obsession, at least as far as attraction between two people, cannot last---it flares up and dies down fairly rapidly. Anything beyond that is pathological, even though it might remain private and on the mild side.

I also think---and this is purely my own experience---that men perhaps develop something closer to "obsession" (when maybe a better, more accurate way of describing it would be a good old-fashioned case of lust). I know many men who are still slightly obsessed with women from their past---unobtainable women----but I know relatively few women who still carry those same feelings for any one man.

Many psychologists agree with me on this.