Therapy is about you, though. He's basically standing back to make as much space for you to be you as he can. If he jumped in with his opinion like a friend might, then you aren't getting something from him that you couldn't get from a friend, right? For me, therapy is about being able to hear my own voice for once without a lot of outside noise. What do I think? How do I feel?

I have had the experience once or twice of my T sharing something I didn't find interesting or helpful, and it's frustrating to sit there listening to her talk when therapy time is already so limited. Plus, maybe there are things about her personality or her life that are complicated or that conflict with my values (maybe not her feelings about cats, but important things), and it wouldn't really serve my purposes in exploring myself and my worldview to have to deal with something about her that I find disquieting.

That all said, I think it's worth talking to him about this. I'm guessing you have good reasons why you want more self-disclosure from him, especially since it keeps coming up. Why is that? Do you want to feel closer to him? Are you frustrated by the power differential, that he knows a lot about you and you know very little about him? What are you dying to know and why? I have found that my need for extra information about my T (mostly through extensive googling) dropped off to almost nothing once I started to be able to trust her and our relationship and the care I feel from her in session. It wasn't really about needing to know her favorite color or her blood type after all. So maybe this is the same kind of thing for you.