Freedom of speech is between a person and a government, not between a person and a private club they pay yearly dues to be a member of.

The confusion is that in the US the professional organisations are a part of the government. In Canada, the government gives authority to private groups to manage themselves, and they basically get to be in charge of a job title. Jordan Peterson doesn't practise psychology anymore and hasn't for nearly a decade.

Yet he's kept his professional membership going. This way, he can say "As a psychologist, I think [some bullshit about something that has nothing to do with psychology]." This is more than enough for the College to properly reprimand him, as he's bringing the entire profession into disrepute - but they didn't even do that, they just asked him to attend a couple courses.

He could always quit the profession. He'd still have all the qualifications and accomplishments, he'd just have to talk about it in the past tense, ie when he was actually relevant.