It is not appropriate. He's playing games. He has the ability to say, "I know you are curious, but I cannot and will not answer those kinds of questions." Sometimes people just need to have some boundaries (I'm talking about the therapist, not you.) He's not doing that because he's getting something out of this.

This game of Q & A needs to stop and the focus needs to get back to you and your therapy. If he can't or won't do that, RUN!