I couldn't remember if you are in the US or elsewhere, IRL, but here in the US, your therapist is not obligated to continue to see you if she terminates in a therapeutically dictated manner: She offers a termination session(s), documents in your file and informs you of the reason(s) for termination and she gives you a list of appropriate referrals for continued treatment. If she did all these things, she would not be held liable if you deteriorated or hurt yourself. I say this because on occasion, therapist's recognize that the therapeutic relationship is NOT working and might actually be damaging the client. She would have to show through her documentation in your file her attempts to "get therapy" back on track and the failure of this happening. (Your emails to her would be solid documentation to be included in her file to show this as a reason to terminate). You don't have to agree with this outcome and neither does your insurance company. Your therapist is ethically bound to make this decision if she feels that your continuing to see her is actually hurting you clinically. From the sound of how you describe things in your relationship with your therapist, it doesn't sound too crazy to say things are really off the rails and you might need to start in a new place with a new person. But that has to be either you to decide or your therapist to initiate.

I also wanted to suggest you might want to check out some reading material on people with BPD in therapy. How you react to your therapist is pretty classic--you get angry and lash out (cold anger and rejection of her caring) or acting out (abruptly leaving sessions). The follow-up to this behavior is to make contact with the person in some shape or form, (you tend to do this in emails--writing eloquent and heart felt emails, pouring your heart out and talking about having a significant revelation) offering yourself up as the one who is "bad" or inappropriate in your previous reaction to her. It's like offering yourself up on the alter of shame, attempting to reconnect by being the naughty child who had a temper tantrum. People with BPD often demonstrate this behavior with their therapist and/or their loved ones. If the person accepts the attempt at reconciliation, then things might be calm or relatively calm for a short period of time and then things heat up again, leading to more anger and resentment (fear of the person planning to leave or abandon).

Probably the worst thing for you therapist to do is respond to you through email. It's fine for you to write them, but the actual content needs to be dealt with face-to-face. You've already talked about how you tend to "read her mind" or her facial expressions and it appears that you often project or put your own spin on what she's thinking. If you do that face-to-face, I think it's even easier for things to get in a big hot mess through email. Talk about you emails with her in session! And if she is able to do that with calm warmth, interest and understanding (not cold withdrawal), perhaps you two will work things out. But please, please, please don't expect a significant or in-depth response in an email from her. Some people can do email therapy but a lot of people can't . . . you appear to fall into the latter category. Just my thoughts on the emails.