It's like a heart surgeon claiming architects have building design all wrong.
FWIW, I have no context on the specific claims made by Peterson, but I've increasingly seen a line of logic that suggests you need to have a PhD in a topic in order to think critically about it.
Sample Weather Channel Guy: - No history in psychology - Citing papers that are not highly respected under peer review
Sample Psychologist: - Has a long history in the field - Ideally has references available for their own claim
In this case, you'd probably want to err on the side of trusting the second person in the chart. What didn't happen, though, was a complete dismissal of the first person's claim based on credentials alone. If you have to make a decision on something quickly and authority is the only way for you to judge it, then sure, go for it. But appeal-to-authority doesn't belong in open-ended debates.
You can claim he giving another side to the "Mainstream media", but does he give in depth interviews with scientists who are little more than quotes in the media? or is he more focused on giving the "Other side"
Eg, he just had that idiot Peterson spouting climate rubbish, has he had credible climate scientists on his show?