Hi, Ariesmars!
Guess: Whether or not your T personally desires to be your friend, she may (probably?) feels she must maintain a respectful emotional distance from you in order to maintain a professional therapeutic relationship with you. She may want you to want friends, but perhaps feels if she opens herself to you it will distract you from attempting to make friends "on the outside." Maybe she's using emotional distance to "nudge" you to seek "real" friends who don't have anything to do with your therapy.

This is all speculation on my part and realize it probably won't make you feel any better about what's going on. Ariesmars, you deserve friends.