In her linked Slate article (that she authored) she said (about Peterson)
"[Peterson] became hugely popular following his swift rise to notoriety in the fall of 2016, when he refused to comply with university policy on addressing students with preferred gender pronouns." He publicly stated be had no issue using preferred pronouns, but his non-compliance was with Canadian federal Bill C-16 which forced their use and he felt was 'compelled speech' therefore unconstitutional. He framed it as a free-speech issue, but his opponents tend to frame him as a bigot who doesn't respect trans rights.
The problem is that Peterson himself misrepresents the situation. The bill simply classified trans people as a class similar to racial or religious minority. Meaning don't discriminate. It wouldn't make it illegal to misgender someone per se. Like walking down the street or by accident, but as a teacher to repeatedly and knowingly misgender a student you are pretty much by definition harassing and discriminating against them. Its basic common sense, but he tries to pretend it's a free speech issue. He's invented an innocuous sounding argument for allowing harrasment and discrimination against trans people and its allowed him to tap into a general anti-trans sentiment which runs deep through conservative culture which has resulted in fame, wealth, and notoriety.
Think it's kind of dark.
"[Peterson] became hugely popular following his swift rise to notoriety in the fall of 2016, when he refused to comply with university policy on addressing students with preferred gender pronouns." He publicly stated be had no issue using preferred pronouns, but his non-compliance was with Canadian federal Bill C-16 which forced their use and he felt was 'compelled speech' therefore unconstitutional. He framed it as a free-speech issue, but his opponents tend to frame him as a bigot who doesn't respect trans rights.