Trying to help is not enough. If something/someone isn't helping then why would you continue? Fault-finding is not all that useful. You are "doing" something if you fired your T. I don't know who said or how you came to believe it was "you" not trying to help your depression but I kind of doubt that is 100% true as our "body" self has its own ideas of "life" and what is needed to sustain it that our heads can't necessarily see/override. It could be that not seeing progress with this T was depressing you further and so firing her was a "good" thing.