My T only self-discloses in the context of conversations we're having. Once we were talking about needing to be liked, and he was saying that it's impossible to have
everyone like us. As an example, he said that another T he had collaborated with for quite a while decided she didn't want to work with him anymore. He asked why, and she said "It's your personality."

That must have been an "ouch" moment, and he made no attempt to hide it, but just shrugged his shoulders and said something like these things happen and we can't please everyone.
These disclosures not only drive a point home but make him more human to me, and not just an authority figure who's preaching to me. He lives life too.