even with the clarification, i think this T is missing the point of therapy...
you are seekimg her help trying to change something, though you have little internal hope of changing it. As a T wiith a new client, I would hold their hope for them until we can either determine it's hopeless (HIGHLY unlikely) or they can find their hope... Just you showing up to therapy says that you at least want to change something, even if you belive the change to be unlikely.
I would still try to find another T. This one seems to buy into your self-assesment of hopelessness, and that's pretty crappy of her to do (especially not knowing you). If she is willing to give up before you even get started, what's going to happen when you hit a bigger bump during therapy?