What's so troubling about this is less about the discontinuation of the hugs, but the way he has pathologized you and can't even see his reactions as harmful. That is why I would strongly urge leaving this guy. There are therapists out there who don't do this. They really don't. He lacks insight. Not a good look for a therapist. He is the one who has painted you into a corner so that whatever you do, it's your "borderline" coming out.

If I were you, I would think long and hard about whether or not I could ever feel good about myself with a therapist like this. This goes way beyond the hugging issue.