Just another thought and one that I've considered as a possible reason for my obsessing:

Could it be that obsessing over people this way is some kind of distraction from some other issue your subconscious is trying to protect you from facing in therapy?

For example, in my own search to find answers for why I obsess over Ts I've read that it can be a distraction from the real issues that brought you into therapy. While I disagree with this as a comprehensive explanation for the obsessing (there are many more reasons besides) I do see this as being partially true for me because however painful it is, obsessing over T (or whoever) is the lesser of two evils. It is much more painful to start to unpick why I'm obsessing and explore the unmet needs and the void that I'm trying to fill with an unhealthy attachment.

Secondly, could it be a coping mechanism? Do you find that the more anxious/depressed/stressed etc you feel the more you obsess after people? Sometimes in the height of my despair, I find obsessing over someone to be of some comfort but more often, it's perhaps the pain it causes me torturing myself this way over unavailable people that I find more comforting....or should I say familiar? What I mean is, it's a familiar feeling to me to torture myself by obsessing over people so perhaps I find comfort in the familiarity of that feeling.

Anyway, does any of that resonate with you?