I'm not sure I understand his approach. Thinking back to his thing about twice weekly sessions, I thought "not rewarding the illness" was about not doing things to reward inappropriate, unhealthy, or disruptive behavior. So if you show up at his house at 3 AM, he shouldn't give you care/attention then. If you go to therapy twice a week (adhering to the agreed upon schedule and fees, etc), how is that rewarding you for being ill? That just seems like appropriate treatment.

I don't have BPD, but I do have some borderline traits. I am mostly seeing my secondary T for EMDR, but she folds in some DBT too, which I'm sure you know is the gold standard for BPD treatment. DBT seems much more collaborative than what your T is doing, and it seems pretty big on validation. Having to report in about taking days off and promise to stay out of the house seems kind of intrusive and invalidating, which maybe re-enacts the conditions that gave you the (alleged ) borderline traits in the first place.

I also find that the more I embrace the fact that I have borderline traits, the less shame I feel about them, and the less they flare up and impact my life and my sense of self. Nobody wants to be reactive and have tendencies toward black-and-white thinking, etc. It's almost always a result of trauma and chronic invalidation, which probably nobody would sign up for. So if it isn't your fault, then why do you have to feel shame about having to manage those traits?