At every possible opportunity, in every interview and discussion, he's stated that his problem is not the use of these words, it's the prospect of forcing their use through policy and categorizing this as a form of forcing speech.
I agree with you that overall it's ended up as a net positive for him, at least income and publicity wise.
That's the problem: his speech isn't being compelled. Bill C-16 doesn't compel* anyone[1]. It makes two changes.
1) "gender identity or expression" is added to the list of possible aggravating circumstances tha should be taken into consideration during sentencing. For this to affect anyone, they first have to be found guilty of some crime.
2) "gender identity or expression" is added[2] to a list of "identifiable groups" that might be targeted for genocide. For this to affect anyone they must [318 (2) (a)] "kill members of the group", or [318 (2) (b)] "deliberately inflict on the group conditions of life calculated to bring about its physical destruction". Both (a) and (b) require "intent to destroy in destroy in whole or in part any identifiable group.
If Peterson insists he could be affected, he must either be committing some other crime against trans-people or plotting their genocide. Instead, the simpler - and more plausible - explanation is that he doesn't know what he's talking about.
[1] http://www.parl.ca/DocumentViewer/en/42-1/bill/C-16/first-re...
[2] http://laws-lois.justice.gc.ca/eng/acts/C-46/page-73.html#h-...
Your answer is an actual good faith counter to Peterson's assertions but the part where you quoted me is where I simply state what he's claimed in interviews.
I do this because people usually start out by straw-manning him, claiming he's said he's anti-this or that, whereas I'm claiming he's mainly said that his stance is against speech being compelled by law (which is fair game to argue against, as you did, if you think he's wrong).
I don't have to agree with his arguments to point out when people straw-man them
It's this same gung-ho strategy that leads to the videos of protesters approaching Peterson after shutting down his speeches and smugly asking him "about the neo-nazi" presence" at his event (he of course responds that he deplores them) as cheap way of implying guilt by any sort of implied association.
It's stunningly dishonest to try such cheap association tactics against someone who's spent their career studying and lecturing on the dark aspects of the human condition and how they lead to murderous and authoritarian movements like the Nazis and then sets out frameworks to both recognize and turn away from that darkness.
Edit: to be clear, I don't view your writings in this dishonest lens, the comment was more about the patterns I've seen creep up in general.
I suspect You're employing a little slight of hand here that reads like he's shouting "marxist!" at all professors rather than some professors, that is, the professors who he claims promote that ideology. If he suspects that some professors have that aim, he's entitled to call out what he sees without people painting it like he's screaming at shadows.
We could argue around in circles about this, although I think we might agree on what we're debating.
- He argues that using non-traditional gender pronouns is road to gulags. (paraphrasing your first comment)
vs
- He argues that compelling speech through policy is a road to gulags, and the noun issue at hand happens to be a vehicle in this particular instance.
I'm not saying that I agree with his thoughts on the nouns in question, but it seems that your focus is the hill he chose to stand on, whereas I'd argue that it's important that people stand on hills when it comes to laws that compel speech.
When you say that he argues that people don't have the right to choose their own nouns, I think it's lacking context from his lectures. He explains in his talks that he sees rights as something that become the responsibilities of other people. So in essence here he's simply repeating his assertion that his speech, and therefore his thoughts (if you accept his premise that control of speech is a tool to shape thought), shouldn't be compelled by demands of other people to control speech via policy.
I'd concede that it's not the readers fault that the context is lacking in the writing, and that leaves it open for you to reasonably argue that he didn't make that statement with this context in mind. Anecdotally from watching hours of interviews and lectures, I'd make a claim that the context is important.
If Google's agenda is to promote a progressive worldview, then a highly-credentialed man cultivating attention for rants about how using non-traditional gender pronouns is a road to gulags makes an unlikely champion, even if some of his more nuanced and informed opinions are interesting in their own right.
If Google's agenda is primarily to make ad revenue - which is better supported by the evidence - then having a flagging system and demonetising videos by people that annoy certain sections of society enough to get flagged a lot even if you reinstate them is probably a net positive for the overall value of advertising on Google's network. (I don't think Peterson's income has exactly suffered either; quite the reverse since his Patreon account will have enjoyed the additional publicity)