The key to contrition, according to public-relations experts, is projecting sincerity, humanity, and a plain-spoken demeanor — the better to convince a cynical public. And in this age of whipsawing social media, you had better do it fast.

“The head of United should never have been allowed to take three swings at correcting and apologizing for an incident that was on more social media than Kim and Kanye’s wedding,” said Mortimer Matz, a New York consultant who has guided decades’ worth of clients through crises small and large.

United issued several halting statements about the plane episode, which first emerged Monday morning, before Mr. Munoz made his abject appearance on Wednesday on ABC. Mr. Matz said the airline had missed its moment.

“You’ve got to be a fast thinker in the digital age,” said Mr. Matz, who will be 93 in July.

Many companies now take steps to be nimble and responsive when a furor erupts online. Last week, Pepsi took less than 24 hours to apologize and retract a multimillion-dollar advertising campaign that used populist imagery to sell soda. It was a rapid U-turn that would have been unthinkable a few years ago.

This week, Mr. Spicer was quick to recognize the damage done by his ill-considered remarks, which prompted immediate denunciations on Twitter as well as calls for his resignation. He appeared on CNN within hours of his gaffe, while Mr. Munoz waited two days.