could be a trauma response - like I used to date a girl who became a hoarder because her mother always took her shit away as a child (I sat at a Waffle House with this girl until 3 AM bonding over our mothers)

I think it comes together with a some type of mental disorder or illness

For me, it was like what LaDama said. I've been prone to obsession when my level of anxiety has been high, as well as being depressed. It's some weird way the mind tries to cope, but for me it just made things even worse.

I think it starts as some sort of coping mechanism for anxiety.

Probably boredom like someone else said, or in the case of a person, maybe someone feels theres unfinshed business with the person.

The short answer is boredom, the not so long answer is boredom + smartness + tiredness. Though such a wide variety of obsessions might hint at different reasons, and if that's the case I don't have enough experience to analyse it.