Yes, I agree with this. It's up to the therapist to decide on and hold the boundaries about what they will and will not disclose. The client should be able to ask pretty much anything, and it's up to the T to decide if they want to answer or not and how much information to give. Like if a client asks if a T has kids, the answers could range from "I prefer not to answer" to "yes" to "Yes, I have 2" to "Yes, I have 2, they're ages 8 and 10" to "Yes, I have 2, Timmy is 8 and Katie is 10" (I picked those names randomly). And to potentially give more info about them, as my ex-MC did (by choosing to disclose on his own throughout sessions, not in response to my asking).

My T said he had a son, and I asked his age. He told me his age then pointed to his picture on his desk. As far as other questions, he's said he wants to protect his privacy, and I've respected that and not asked any more. (It's sort of complicated by the fact that my ex-T told me something fairly major about current T's son before I started seeing him, which is something in common with my daughter. I eventually told T what she said, and he didn't dispute it at the time I shared it, but then it sort of became an issue later on when I brought it up and he said she may not have had accurate information. But that's an entirely different story...)