Hi Nightsky,
I am sorry you are feeling this way about your therapist. I have my own stories of feeling stuck and not trusting my therapist but for me at least, by the time I can write about it like this it means, I made sense of it.
To me I find when I give a feeling to the therapist like I feel he is angry at me, I investigate my own anger from today or from my trauma and my past...and boom I am in that rabbit hole of my anger. If I feel he hates me again. I start to investigate that I probably hate myself for not taking care of my trauma for a long time or my mother who did this to me and again...I go in that rabbit hole and come out the otherside exhausted but having a much better idea.
I think (and this my take on reading your post), someone convinced you that you are a liar or will be a liar at very early time in your life. That person who convinced you that you are a liar or will be liar is a person who is truly close to you maybe even still in your life and you somewhat disconnected so much and so far that you cannot believe this can be!
But one thing is certain you can feel anyone will think you are a liar but does that matter at the end of the day? if at work a coworker says yeah Nightsky you did this and you did not, will you have hives or panic or cry? I do not know you but I would think at work, especially knowing this is not true, you would be like wow! this woman is f--ked by saying this and would correct and move on.
But now, because of therapy and you are sharing real stuff with this person, you are feeling exposed. That exposure is from your past and has no relation to the therapist any shape or form. She is your target, your mirror, but she has not given you a reason to believe you are a liar. What she did, is she gave you a way a feeling that you can trust her just like the person (in the past) who also give you that feeling of trust and then betray you. So you trust the therapist and that person and only one of them convinced you that you are a liar or will be a liar. I think on a good day, you will know for sure who that person is.
I am sorry if my description is triggering or crossing boundaries. I am trying to reach you from far away via by writing and trying not to write too ambiguous or allegorical.
Please tell your therapist you feel this way and let it out so you can focus the source of this issue. You are safe with your therapist and you are safe now because you are here now not there anymore.
All the best.