When I think about when I speak to someone and that someone expresses some liking about something then I typically don't really think about how I like that thing. If someone tells me that he likes cats then I'm more than happy to talk to him about his cats without really considering if I like cats or not - that just doesn't seem relevant to me at that time. I imagine that in therapy it is little bit like this for the therapist - if he is focussed on your liking to cats than his own likes or dislikes are not in the forefront of his attention and he may not even remember that he himself doesn't like cats that much. Because his personal opinions are just not that relevant at this moment. I can even imagine that when you ask him if he likes cats then he might even have to think a bit to find his own likings again to come out from the intense focus he maintains on you.

Also, I personally feel the more useful self-disclosure comes with being together with the person - seeing/sensing how he reacts to you, how he responds to you, how he understands and interprets the things you say to him. Compared to that, factual information really gives very little info about the person imho.

But I also think that you should discuss all that with him ad nauseam until it all starts making sense to you (I for instance return to the question of why I am in therapy and what my T can possibly offer me regularly at least once a week).