I feel like he shows me who he is in his interactions in the therapy room. I feel like I know him well without having biographical information about him. There's more to knowing someone than knowing facts about their life I think. I personally would find it offputting if he brought too much of his unrelated thoughts and experiences into the room.
This is clearly troubling for you though, and I think it's probably something that is useful to discuss in therapy with him. Is it the power dynamic that troubles you? If so, what other ways are there to explore the power dynamic and reduce its discomfort for you?