rebnsof,
That's a very peculiar request for a T to make (imo). I've seen MANY T's in my life and haven't ever been told that I need to be obsessive with them.

WTH??
Yes, you may need to open up, but he/she should wait until you feel safe enough to open up to that level of trust naturally.
I don't like that at all. I hope that you reach a safe and comfortable relationship with your T soon.