You are bad at analogies. Hopefully, the analogies you use in your professional life are more on point.
The reason lawyers can't insult and and swear at judges is because lawyers have a prefessional duty to uphold the integrity of the entire justice system - even when it isn't working correctly. In order for people to keep hiring lawyers, above all the justice system must continue, or there will be no lawyering to be done. That's what that prohibition is about - protecting the institution that is the raison d'etre of the legal profession. In fact, you're a very good boy here on TERB, constantly defending the work of the justice system, even when it amounts to defending the indefensible.
Peterson was not brought up on discipline because he made statements attacking the integrity/reliability of his own profession. Instead, his professional body decided that no client should be aware of a practicing psychologist's view on certain social/political subjects - not that psychologists couldn't hold such views, but rather that no client should be made aware of them. There is NO comparison between that concept and the concept of protecting the idea that the work done by the profession of psychologist is reliable and helpful work.
Now, I might take issue with whether psychologists do useful/reliable work, especially given the specious reasoning of their professional body, but that's not what Peterson did.