Hi Sally,
I'm really sorry this is happening! This totally sucks.
If it was me, this would make me crazy and feel totally unsafe in therapy. It's hard enough for me to tell someone I didn't like what they said or it upset me or whatever, and then to have the therapist just defend themselves would be too much. And I couldn't take having to go through the whole emotionally draining process of threatening to leave either!
I had a little bit of this go on with me with a previous t. I was going through so much with family issues, reporting emotional abuse to professionals in my sister's life, trying to figure out safe living options for myself for after college ETC. My t said time and time again when I would ask for help finding resources about all this," I'm not a social worker. What you're asking me to do is casework." The real kicker for me was when I applied to the state department of mental health for services, and she'd never heard of them and had no idea how to fill out the forms, or even how to write a five axis diagnosis! And her response when I was frustrated about this and even crying was, first to not even notice that I was crying, and second to say," Why would I know about this? I don't work in a clinic!" She was totally flustered about having to fill out the forms, and again kept saying she wasn't "set up" to do this kind of thing.
So I left her. We'd been working together for over a year, but I couldn't take that kind of attitude. If I were you I would leave and find someone who could admit when they were wrong and not play this stupid game, and actually take responsiblity for their own issues. But that's just me.
Please keep us posted!