This isn't directly relevant, but a more convincing hypothesis for why psychologists are depressed is that non-neurotypical people are more likely to be interested in psychology.

An even more convincing hypothesis is that depression is simply contagious. (That is, hearing a depressing thought can be almost as depressing as coming up with it yourself.)

Edit to add: NLP co-creator Richard Bandler claims to have invented the practice of "secret therapy" specifically so that he wouldn't have to listen to depressing thoughts and become depressed by them. (Secret therapy consists of telling clients something like, "I'm a mathematician, not a psychologist; so it's against the law for me to listen to your problems. Just call the problem you're having "X". When do you experience X?"... and proceeding to troubleshoot the structure and process of the problem, rather than its content )