I agree with Jane T. I have sent an email and a text to my T explaining why I was quitting. I realised after sending the email that I wanted a response from her, that was why I had written my thoughts. I therefore didn't quit, I went to my next appointment to discuss (she doesn't discuss things by text or email), and I didn't quit after all. I don't know if this applies to you too - if you email her if in some way you are looking for a response (maybe some shred of understanding?) from her? If so, then emailing your thoughts is not quitting, it is carrying on.

I identify with you going in to see her to express yourself rather than simply walking away - I did that too with my T the first time I wanted to quit, I decided to go in and tell her how angry I was first - I wanted to face up to someone, perhaps for the first time in my life. I think my T probably responded differently to me than your T did to you.