This is temporary and part of therapy.
In any relationship, one party can ask a question and the other can choose whether to answer it, or how to answer it. We all have this ability to set boundaries.
T's boundary about disclosure are fine. They don't feel good, but they are fine.

But definitely keep talking about this, how you feel about it.
His reply to your asking is making him seem cold, and his not providing the specific answer to your question makes him feel untrustworthy, but it is not his intent. His intent is to respect the boundaries he chooses for himself, while recognizing your curiosity.