Why do we get obsessed with people ? For example, last night I had a dream where I was with a person who I haven't even seen or thought about for 2 years, and in the dream were in love with each other. Today I can't stop thinking about this person. This has happened before, and I know people get obsessed with celebrities because they are rich and famous, but i've never had this kind of dream with a famous person in it.
One possibility is that you're not so much in love with the person as with memories you have of them, or memories of the time when you knew them. It isn't the only explanation, of course, just one.
Sometimes obsessions come about as a way of distraction. Sometimes the person can be aware of it, or it can be that subconsciously that person is infatuated with someone and spends all their time thinking about them etc, to distract from their own problems/life/loneliness. As jjf2003 says, its just one suggestion, as its different for everyone.