For someone who’s become rich and famous for his speech, Jordan Peterson spends a lot of time saying, “that’s not what I said.”

A clinical psychologist and scholar, Mr. Peterson has taken the Internet, along with the publishing and speaking-tour worlds, by storm. His lectures and books now command enthralled audiences worldwide. Fresh off sold-out appearances in Australia, a 12-city North American tour to promote his latest book started Sunday in Manhattan.

But away from the crowds, his point of view isn’t always welcome. Whether it’s a confrontational interview with the U.K.’s Channel 4, a haughty dismissal in The New York Review of Books, or an inability to get listed on The New York Times’ best-seller list, the media gatekeepers seem to want Mr. Peterson kept outside.

“That’s because he’s a massive threat to them,” said television news host Tucker Carlson, who added he’s enjoyed every appearance Mr. Peterson made on the host’s Fox News Channel program. “That’s all an effort to make him be quiet.”

Thus far, the effort earns an “F.” Mr. Peterson’s “12 Rules for Life: An Antidote for Chaos,” is a runaway global best-seller. Months after its publication, the book sits at No. 2 on Publishers’ Weekly nonfiction list, and on Amazon it still holds the No. 2 spot in all books, while ranking as No. 1 in three categories. On YouTube, the 225 lectures Mr. Peterson has posted have attracted more than 460,000 subscribers and 30 million views.

Exactly what Mr. Peterson imparts in his speeches and prose isn’t easily classified. His website proclaims his new book, “shattered the modern commonplaces of science, faith, and human nature while transforming and ennobling the mind and spirit of its readers.”

He jumps nimbly among multiple sources, from mythology to history, and from literature to psychoanalysis. There’s talk of “archetypes,” and a resurrection of themes that last held sway when disciples of Sigmund Freud and Carl Jung ruled the academy. His books are nonfiction, yet they are also self-help with more than a dash of philosophy.

Mr. Peterson’s public relations team said it could not arrange an interview with him as he embarked on his speaking tour. But his rise is easily tracked on YouTube: from the young Peterson at Harvard, talking about Alexander Solzhenitsyn with minimal production values, to a more assertive and confident professor teaching mid-level classes at the University of Toronto, to a kind of new-age guru appearing solo on stage before a rapt audience.

Mr. Peterson’s philosophy boils down to what he describes as a mature attitude and concomitant “competence.” While much of what Mr. Peterson dissects is universal, he often addresses himself to younger men and what he calls “a crisis in masculinity.”

In a famous Channel 4 interview last January, Mr. Peterson said those that don’t grow up, “are left bitter and resentful and without purpose and adrift, and hostile and resentful and vengeful and arrogant and deceitful, and of no use to themselves and of no use to anyone else, and no partner for a woman and there’s nothing in it that’s good.”

Much of what he says can be chalked up to common sense. His sixth rule for life, for example, tells readers to “set your own house in perfect order before you criticize the world,” which to some ears may sound a lot like stone throwers residing in glass houses.

“It’s a delineation of the kind of destiny that makes life worth living,” he says.

But it has been his refusal to kowtow to modern liberal pieties that has made him a star or a marked man in certain circles.

Consider the first event that thrust Mr. Peterson on to the big stage. In 2016, the government in his native Canada pushed Bill C-16, dubbed the “Canadian Human Rights Amendment,” that sought to order people to use newly created pronouns.

Mr. Peterson said he was happy to call individuals by whatever pronoun they preferred, but he would not abide government commands over language. He testified as such in Ottawa, and his opposition to the law earned the ire of transsexual activists and much of Canada’s left-wing for something that is still misinterpreted.

To be sure, his stance earned him support, too, as has his unstinting attack on the modern intellectual gospels of Marxism and postmodernism.

“He asks tough questions about the empirics behind many commonly held but not deeply understood beliefs and so in my mind is merely bringing intellectual rigor to a number of important issues,” said William Watson, an economics professor at McGill University and a prominent public intellectual in Canada. “I do admire his courage for expressing reservations about intellectual trends that many people probably harbor but prefer to keep to themselves, for fear of the social media mob.”

It was yet another misinterpretation of Mr. Peterson’s prose and speech last January that sent his reputation to new heights.

In an interview with the Channel 4’s Cathy Newman, she adopted a relentlessly adversarial stance toward Mr. Peterson and unfailingly twisted his words. Nevertheless, Mr. Peterson remained calm and patiently refuted Ms. Newman’s interpretation time and again.

For example, Ms. Newman said Mr. Peterson had refused to call people by their preferred pronouns and Mr. Peterson noted that is not what he had said. He is perfectly happy to call people by their preferred pronouns, he just won’t allow the government to dictate the matter.

Eventually, Mr. Peterson grew so exasperated he chided Ms. Newman’s hearing.

“No, I’m not saying that at all,” he said at one point in the interview that’s now been viewed more than 8.4 million times. “That’s because you’re actually not listening.”

Such misinterpretation must be deliberate he intimated because he is “very, very, very careful with my words.”

The interview went viral and Ms. Newman complained when some of Mr. Peterson’s far-flung fan-base attacked her on social media. The interview also garnered some chin-stroking about the alleged shortcomings in Mr. Peterson’s communication skills.

New York magazine felt compelled to explain to readers what it assumed would puzzle them in a piece titled, “Why they listen to Jordan Peterson.” In a piece that broke down some of the exchanges between Mr. Peterson and Ms. Newman, The Atlantic asked, “Why can’t people hear what Jordan Peterson is saying?”

All of those stories, however, took Mr. Peterson and the phenomenon of his popularity seriously. The same could not be said of the New York Review of Books, which this month took careful aim and tried to deliver a headshot in a piece by Pankaj Mishra that ripped Mr. Peterson for his alleged “mystic fascism.”

Mr. Mishra began with a characterization of Mr. Peterson as “an obscure Canadian academic,” and then rolled out the heavy artillery and started blasting.

When the dust cleared, the NYRB audience was left with an image of a flaky writer only popular with dim-witted right-wing men and the latest manifestation of a possible return of Adolf Hitler and another Holocaust.

The response to Mr. Mishra’s philippic came swiftly, with several people, including Mr. Carlson, noting they had never heard of him.

Uncharacteristically, Mr. Peterson lashed out, too, tweeting that Mr. Misha was a “sanctimonious prick,” and offering to slap him silly.

“The key to him is his fearlessness; his unwillingness to accept the Left’s premise that they’re virtuous and you’re not,” Mr. Carlson said. “Isn’t that exactly what our campuses should be producing?”

Having enemies on campus or on the NYRB staff only burnishes Mr. Peterson’s status with many fans, who have come to look on his lectures and speeches the way people used to look at Beatles songs. His Twitter reaction, however, surprised some of them.

“Although I don’t agree with all of JP’s ideas, I still respect them,” Dr. Kendall Conger, an emergency room physician in Raleigh, N.C., wrote in an e-mail. “He has been saying that he most worries about misspeaking or saying something bone-headed. [The tweets at Mr. Misha] is his first misstep (not in content, but in delivery).”

Dr. Conger recently joined a study group dedicated to Mr. Peterson’s videos and books and those he often touches upon have bloomed. The founder of that group, John McGlone, found himself Sunday night in the third row at the Beacon Theater on Broadway as Mr. Peterson’s speaking tour began.

“I really love the way he talks about free speech not only as a political right but as a mechanism to think,” Mr. McGlone said.

A 29-year-old IOS engineer, Mr. McGlone is hardly the kind of alt-right radical Mr. Peterson’s detractors claim comprise his fan base.

Mr. McGlone considers himself a classical liberal, and he resents those who try to pigeonhole his or Mr. Peterson’s thinking. His study group’s co-founder is a woman, evidence that Mr. Peterson’s audience isn’t exclusively male.

Mr. Peterson said that was always the goal.

“I’ve been telling young men but I wasn’t specifically aiming this message at young men to begin with it just sort of turned out that way,” he told the BBC’s Ms. Newman. “People have this capacity within them to set the world straight.”