I am not expecting this to be a popular viewpoint, but I am actually with the therapists here. It is about the client. And a danger of talk therapy is it becomes about the therapist. A lot of abuses and pain in therapy occur when the therapist becomes the focus, not the client. Good therapists will keep that in mind.

It's fine to care human to human, no one expects otherwise, but it's like if my students notice if I'm off or sad one day. They don't bring it up and neither do I--it will interfere in both our roles in that relationship. (Whereas if they seem off or sad, it might well be my job to bring it up depending on the circumstances.) I did mention my mother to my students, but that was to explain some changes I had to make to the classes, not to invite their concern. What I'm saying is that of course a client will likely notice if a therapist is off, but if their goals in therapy are to work on themselves, the best thing they can do for both themselves and the therapist is maintain that focus and not shift focus to the therapist. Not bringing it up doesn't make you cold or uncaring; it means that you realize you are the most important thing in your life.

It would be different with a friend or co-worker you noticed was off, and therapists are neither.