United Airlines on Tuesday faced a spiraling crisis from videos showing a passenger being dragged off an airplane, as consumers threatened a boycott of the airline and lawmakers called for an investigation. By the afternoon, after more than a day of changing statements, United’s chief executive apologized and promised a review of its policies.

“No one should ever be mistreated this way,” Oscar Munoz, the company’s chief executive, said in a statement.

But the videos had already cast an unwelcome light not just on United, but on the airline industry’s efforts to maximize profits. As companies push to make money from baggage fees, seat reservations and other services that were once included with a basic plane ticket, the videos added the potential for an even harsher indignity: sitting in a seat with a ticket and getting physically ejected from the airplane.

The passenger, Dr. David Dao, was identified late Tuesday in a statement from his lawyers, who said he was undergoing treatment in a Chicago-area hospital for his injuries. Some videos had showed him with a bloody face.