Jonathan Haidt let his son walk half a mile to school by himself in fourth grade, two years before any of the boy’s classmates did. He gave the 9-year-old a hand-me-down iPhone and watched nervously on his own phone as his son crossed a busy intersection in their Greenwich Village neighborhood.

A few years later, when Haidt’s daughter was in fourth grade, she didn’t get an iPhone. That was 2019, and concerns were growing about kids’ phone use. Instead, he got her a GPS-equipped Gizmo watch so he could monitor her walk to school.

Haidt, a social psychologist and professor at New York University’s Stern School of Business, has since done extensive research into the subject of children and smartphones. His conclusion has turned him into a high-profile critic of one of the world’s most lucrative industries, as he argues that the giants who brought us smartphones—with their round-the-clock entertainment and social media—are the primary cause of the rise in anxiety and depression in adolescents.

Haidt’s position, laid out in his new book, “The Anxious Generation,” has thrust him into the escalating debate over kids and phones.

Haidt says his objective is to unite parents to take collective action, because they often give their kids phones and social-media apps due to peer pressure. “My goal is that no parent who wants to do the right thing will be the only one doing the right thing,” he said in an interview.

The book has topped the New York Times bestseller list for hardcover nonfiction every week since it came out in late March. It is the talk of mom group chats. Oprah Winfrey praised it, so too celebrity moms like Jessica Seinfeld . Arkansas Gov. Sarah Huckabee Sanders , a Republican, on Monday sent copies to all state governors and to members of her state legislature with a letter calling on lawmakers to protect kids from the “dark sewer” of social media. Haidt is so busy promoting the book and fielding inquiries that his automated email response says he won’t be able to reply until his book tour ends in August.

A review in the prestigious journal Nature says there’s no evidence to support his theory and accuses him of fearmongering.

“Worse, the bold proposal that social media is to blame might distract us from effectively responding to the real causes of the current mental-health crisis in young people,” Candice L. Odgers, a psychology professor and associate dean for research at the University of California, Irvine, wrote in Nature.

Odgers, who has studied adolescent mental health for 20 years, said in an interview that mental health problems stem from a complex mix of genetic and environmental factors such as gun violence and economic hardship.

TikTok, Snap and Meta , the parent company of Instagram and Facebook, declined to comment on Haidt’s findings.

Some 57% of female high-school students reported persistent feelings of sadness or hopelessness in 2021, up from 36% a decade ago, according to a biennial survey released last year by the Centers for Disease Control and Prevention. Among teen boys, feelings of hopelessness rose to 29% from 21%.

Free-range childhood

Haidt, 60 years old, grew up in suburban Scarsdale, N.Y. He spent his days riding bikes and going on neighborhood adventures with friends. It was important to him and his wife, Jayne, to give their children the same kind of freedom.

After studying philosophy as an undergraduate at Yale University, he had a short-lived job as a computer programmer, which he found boring. He decided he wanted to become a professor and got a Ph.D. in social psychology from the University of Pennsylvania.

A temporary teaching job at NYU turned into a full-time and eventually tenured position. He and his family settled in the Village, where he felt his kids could have a free-range childhood. Suburban parents are hesitant to let their kids go to the park alone because someone might call the police and report an unattended child, he wrote in his book. “In Manhattan, nobody would think to call the cops on an 8-year-old out on his own,” he says.

When his children started walking to school, he only tracked them on their devices for a couple of days before his anxiety subsided.

Writing books on hot-button topics became his forte, beginning with a book about happiness and then another about why people are so divided over religion and politics. During the process of researching a book about the fragility of U.S. college students, “The Coddling of the American Mind,” he began wondering about the mental health of younger students.

He met Jean Twenge, a San Diego State University psychology professor, at an academic conference in 2017. Her book, “iGen,” about the unhappiness of children in the smartphone age, had just come out and she was receiving the kind of backlash he’s getting now.

Twenge had been gathering data on the rising rate of anxiety and depression among teens and collaborated with Haidt in assembling the research that formed the basis of his latest book.

While tech has rewired kids’ brains in unhealthy ways, Haidt says, the social platforms had help from two concurrent trends: the decline of free play and the rise of overprotective parenting. Parents who rob their children of the opportunity to solve problems on their own prevent them from developing grit, he says. The popularity of social media and videogames means kids spend more time on screens, communicating with friends—and strangers.

Haidt concluded that four things can be done to create a healthier childhood: keep kids off smartphones until they’re in high school, don’t allow social media before age 16, keep phones out of schools, and encourage more unsupervised play.

He gave his kids phones earlier than he now recommends—his daughter got one in sixth grade—but he held firm on his no-social-media-before-high-school rule, even though both children asked for Instagram in middle school.

His son, now a 17-year-old high-school senior, and his daughter, a 14-year-old freshman, follow the house rule of not having their phones in their bedrooms at night.

Correlation vs. causation

Haidt began publicly posting the research he referred to in his book in 2019—and has been facing off over it ever since. “I’ve been very clear to point out which studies show correlation and which show causation,” he says.

Much of Haidt’s book focuses on girls. He says they have been more hurt by social media than boys. A chapter in his book explains how boys have taken a different path to anxiety and depression, isolating themselves with videogames and accessing porn on their smartphones.

“I’m a big fan of his but where I come crashing down is his claim for scientific proof of a direct causal link between social-media use and teen-girl depression,” says Aaron Brown, a former Wall Street trader who teaches statistics and math classes at several universities, including NYU.

During a live taping last month of “The Reason,” a libertarian podcast, Brown sparred with Haidt over the research on which Haidt based his conclusions.

Brown said that only 22 of the 476 studies in Haidt’s book contain data on heavy social-media use or serious adolescent mental-health problems and that none have data on both.

“It’s legitimate to say most of the studies are weak, and that’s true in most areas of social science,” Haidt says, “but he had such a high bar for proof that he said none met his standards.”

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Write to Julie Jargon at Julie.Jargon@wsj.com