Sounds to me like he wants to be available but can't actually deliver - and is having trouble admitting (to himself) that he can't actually deliver. And you're suffering because of it.

I've done similar things in my professional life when I was overeager to help. Didn't make this morning's class and need to set up a meeting to go over what you missed? Well, I don't have time to do that, but I do have another class starting in 13 minutes - why don't you just come to that one?!

I was trying to be helpful within the confines of my schedule without realizing how stupid/confusing it was to be on the receiving end of my efforts. Sounds like your T was doing something similar.

If you don't dump him altogether, maybe you and T can have a conversation about his availability - his actual availability, not what he wishes he could provide - and how/whether he can help you meet your therapy goals.