Korean Air and Ms Cho, who is in charge of cabin service, apologized. She said her actions were "excessive" and she would resign from all her posts at the company.
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Local media said Ms Cho screamed at a crew member on the South Korea-bound flight for serving the nuts in the first-class cabin without asking if she wanted them. She then questioned the chief flight attendant about service standards and, unsatisfied with his response, ordered him off the aircraft.
Korean Air said flight KE086, with about 250 passengers aboard, arrived in Incheon 11 minutes late after it had returned to the terminal at JFK airport to remove the attendant.
The incident caused anger among South Koreans increasingly uncomfortable about the economic and social privileges enjoyed by the founding family members of big chaebol business groups. They often wield undue influence over management of group companies in spite of their small direct shareholdings.
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Korean Air had earlier said it was "natural" for the executive responsible for cabin services to inspect operations and point out problems, adding that the chief flight attendant neglected procedure and regulations.
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The decision to remove him had been made in consultation with the pilot, it said, and the company would strengthen cabin crew training and customer services.
The airline's explanation caused further anger, prompting the pilots' union at the carrier to say: "Ms Cho abused her position as a vice-president in the process of returning the flight. The incident underlines the mindset of the owner family that they can do whatever they want with the company."
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Lawmakers are also calling for an investigation. "Ms Cho's order of a forceful return could be a threat to passengers' safety by disabling the pilot," said Oh Byung-yoon of the Progressive party and a member of the national assembly's transportation subcommittee.
The transport ministry is investigating Korean Air for possible breaches of aviation safety regulations.
Under South Korean aviation regulations, an aircraft preparing for take-off should return to the terminal only if the pilot determines there is an emergency involving the safety of the aircraft or its passengers. The ministry said it would take action against the carrier if it violated any regulations.