Critics have questioned whether 17-year-old David Hogg and the other high school students demanding that the nation’s gun laws be strengthened are mature enough to understand the complex policy positions they’ve staked out.

But this weekend, Hogg labelled one of his harshest critics using a word familiar to almost anyone who’s ever walked a school hallway: “bully”.

Hogg went on CNN to talk about his latest run-in with Fox News host Laura Ingraham, who made fun of the teenager’s very public lament about being rejected by colleges he had applied to.

“It’s disturbing to know that somebody can bully so many people and just get away with it, especially to the level that she did,” he told the broadcaster. “No matter who somebody is, no matter how big or powerful they may seem, a bully is a bully and it’s important that you stand up to them.”

Poking at Hogg’s comments about his rejection letters, Ingraham tweeted a story from a conservative news site that described the teenager as a “Gun Rights Provocateur” – and said Hogg had not been accepted by four University of California schools.

“David Hogg Rejected By Four Colleges To Which He Applied and whines about it,” Ingraham tweeted. “(Dinged by UCLA with a 4.1 GPA ... totally predictable given acceptance rates.)”

On CNN, Hogg said the tweet – and Ingraham’s criticism of him – was in line with bullying statements she’d made about others: a conflict with gay people while she was at Dartmouth in 1984 and, recently, responding to LeBron James’ political statements by saying the NBA star should “shut up and dribble”.

They also deserve apologies, Hogg said.

James responded to Ingraham during an NBA All-Star weekend press conference.

Hogg’s number of Twitter followers has surpassed 700,000. He compiled a list of 12 companies that advertise on Fox News’ “The Ingraham Angle” and sent a message to his supporters: “Pick a number 1-12 contact the company next to that #”.

In a matter of days, Ingraham lost more than a dozen advertisers, including Johnson & Johnson, Nestlé, Hulu, Jos A Bank, Jenny Craig, Ruby Tuesday and Miracle-Ear.

A short time later, Ingraham apologised, but Hogg blasted the apology as an insincere “effort just to save your advertisers”.

“The apology ... was kind of expected, especially after so many of her advertisers dropped out,” Hogg said on CNN. “I’m glad to see corporate America standing with me and the other students of Parkland and everybody else. Because when we work together we can accomplish anything.”

March for Our Lives – in pictures Show all 13 1 /13 March for Our Lives – in pictures March for Our Lives – in pictures Demonstrators chant during the protest for gun legislation and school safety AP March for Our Lives – in pictures Trevon ‘Tre’ Bosley, 19, of Chicago, the brother of Terrell Bosley who was killed in 2006 in a case of mistaken identity, speaks during the rally AP March for Our Lives – in pictures Marjory Stoneman Douglas High School student Delaney Tarr speaks at the rally AFP/Getty March for Our Lives – in pictures Protestors line the streets in Washington Getty Images March for Our Lives – in pictures People arrive for the March For Our Lives rally against gun violence in Washington, DC AFP/Getty March for Our Lives – in pictures Protestors carrying placards in Washington AFP/Getty March for Our Lives – in pictures Protestors hold up placards in Washington AFP/Getty March for Our Lives – in pictures Schoolchildren wear targets ahead of the rally Getty March for Our Lives – in pictures Attendees congregate in preparation for the march Getty March for Our Lives – in pictures Students brought a host of innovative placards AFP/Getty March for Our Lives – in pictures The movement’s main demand is the banning of assault rifles Getty March for Our Lives – in pictures Since the Florida shooting, students have called for urgent gun reform AFP/Getty March for Our Lives – in pictures In the wake of the Florida attack, President Donald Trump called for teachers to be armed AFP/Getty

Ingraham is off the air this week. She told her Fox News viewers on Friday that the trip is an Easter vacation. The network told The Washington Post the holiday was preplanned.

The advertisers’ efforts to distance themselves demonstrate the influence Hogg and the other survivors of the Marjory Stoneman Douglas High School mass shooting have gained – and companies fears’ about becoming collateral damage in polarising controversies.