What seemingly random things will your T not disclose?

Thought of this question because of something that came up in Monday's session. I was talking about how H and I were considering getting a pet again, so T was talking about the pluses and negatives of various pets--pluses for dogs and...snakes (?!?), more of a minus for cats. At the end of that discussion, I asked him, "So do you have any pets?" He said, "We have a few" but didn't specify, and I felt if I pushed more, he would have held that line. But that's one of those things where it's like...why? Does he think I'm going to run out and buy a matching set of pets? (If one of them is a snake, nope!) Ex-MC was open about current and past pet when we asked him. (Not sure I ever asked ex-T?) This just seemed a natural time to ask because, I mean, he was saying how great snakes can be, so it suggests he either has or had one (or knows someone with one).

Anyway, this is something that I feel would be pointless to push him on, because...what does it *really* matter? But it's just another thing that seems like a huge difference in the T relationship vs. other ones, because if I asked even a coworker if they had pets, I sincerely doubt they'd be like "a few" but not say what they were. Meanwhile, he's mentioned a couple times that his wife has ADHD, which strikes me as a much more personal thing than his pets... And he's shared some other random stuff. He also will never share anything about upcoming vacations, not even something vague, like "I'm going to the Midwest part of theh US" or "I'm going to Western Europe" or if it's a fun or a work trip. That does bother me, but I get the sense it's his boundary that he just won't cross, though he's told me after the fact where he was.

Anyway, just curious as to whether there are any random things your T seems unwilling to disclose (assuming they aren't a completely blank slate T and disclose absolutely nothing).