I don't know your history, so I'm kind-of guessing at it. I can give you an example from my own life. A while ago I had a friend who I really liked and respected. But she pushed for more of a friendship from me than I could give. Eventually, she wanted so much time and attention that it felt like I was being smothered. Like my time wasn't my own. I felt overwhelmed. My friend's behavior began to remind me of my mother when I was growing up. Manipulating and very needy.
By "obsessing" do you mean needy and smothering, maybe?
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