Well, think about it from her point of view. Exchanging emails with you ended up with 1) you sending a suicide email and 2) you calling her essentially threatening to kill yourself in an attempt to coerce her into seeing you again. I'm sorry that sounds pretty harsh, and I know you were in incredible pain when you did that, but it's kind of traumatic to the person on the receiving end and makes them feel helpless. She may have felt like she was not being effective as your therapist because she lost confidence that there was anything she could do to keep you safe when you're sending suicide emails and threatening suicide over the phone. The APA code of ethics, which she is governed by as a psychologist in the US, does say that psychologists must not provide therapy in situations beyond their competency and/or when they are unable to help the client. Right or wrong, that's what the code of ethics says.

I am definitely not a therapist, so I can't offer additional input to that which you've already obtained from the therapists you've spoken with. I did work in a mental health agency for 8 years. I can tell you that in the agency where I worked, a client who threatened suicide over the phone would be moved to a higher level of care. It would depend on the circumstances if they were referred out of the agency due to the threat or not. In your case, I don't think so because you cooperated to keep yourself safe by going to the hospital as directed. If you had made an attempt during/after the phone call and lived, you would almost certainly have been referred out. We also wouldn't have agreed that when suicidal, clients could/should skip their appointments, either. That is the thing that seems odd to me about your former therapist's behavior.