Dad claims he was kicked off jet after tweet

Southwest Airlines (LUV) has apologized to a Minnesota dad and offered him and his daughters vouchers after they were asked to deplane following his posting a negative comment on Twitter. Despite the apology, Duff Watson told CBS News he is not satisfied and won't be flying on Southwest again.

Watson was flying from Denver to Minneapolis last Sunday when he says he got into a dispute with a Southwest customer service agent who wouldn't let his two young daughters board the plane early with him. Watson qualified for priority boarding, but Southwest doesn't offer priority boarding for children.

He tweeted about the incident but says he was then asked to leave the plane with his daughters. He says he wasn't allowed to reboard until he deleted the tweet.

Southwest says that he was asked to leave the plane to resolve the dispute about family boarding policies outside the aircraft. He then reboarded the same flight and flew to Minneapolis.

Watson's daughter told CBS News that the agent threatened to call the police and she was afraid her father would be arrested.

"I was left very upset, very embarrassed," Watson told CBS News.

"We are thoroughly researching the event and, if necessary, will counsel those employees involved," Southwest said in a statement. "For the customer's inconvenience we offered vouchers as a gesture of goodwill."