The snarky rap on psychologists/psychiatrists is that they go into the field because they are trying to fix something in themselves. Probably in some cases.
I think others are just good at listening to other peoples' problems and giving some light on the subject.
I talked with a psychiatrist one time, not as a patient, and he said to me, "You've been in analysis haven't you?" I hadn't, and told him, no. He looked genuinely surprised. Maybe I just looked like I needed it.
He was also an amateur artist, but not a very good one. He had his work around his office, which I thought was kind of interesting.