I think that Ts choose their words carefully and I don't think that he would say something just for the sake of making you feel better because it is his job. I suspect that he does care for you as a client or patient in a geniune way and has the capacity to care for his other clients as well.

I think we all struggle with believing that our Ts care or even that they like us.

I would not test his caring by telling him that you will quit. I have read on this board that people have quit and then end up begging to go back. I think Ts don't question it when we want to quit because it is our life and they trust our judgment.
Letting us go does not mean that they don't care.

I think it is wonderful that your T is supportive and seems to care.