Hi, welcome to PC.

I would find what you describe very difficult, particularly his rather stark change in attitude since you started seeing him. For me, that change would stir feelings of the inconsistent parenting I received as a child, and I would find it destabilising.

I hear that you've tried to talk to him about being uncomfortable with the arguing, and his response was "we're not arguing". To me, he is invalidating your experience here which is unhelpful and not therapeutic. If you feel that you are arguing, what he thinks about it isn't massively relevant imo.

If I were you, I would tell him how you feel his attitude has changed since you started seeing him. You are paying for a service, and part of his job is to reflect on the feedback you give him. If he continues to deny your experience, I would personally see that as a red flag and move on. To be honest, the fact that you feel like you are losing your mind as a result of his denying your reality sounds a lot like gaslighting is happening, and if he doesn't realise what he is doing and change it immediately, I think leaving is important for your wellbeing. Gaslighting is an abusive behaviour, whether he is aware he is doing it or not.

If you think a therapist who better understands your asexuality would be better for you, I think it would be good to search for someone who can meet those needs.

Good luck, I hope you can find what you need from therapy.