"Making drinking accusations against pilots is a serious matter," said Ross Aimer, CEO of Aviation Experts, LLC.

"If you think someone is drunk, you owe it to yourself, your loved ones and other passengers to report it," said Aimer, who is also a retired United Airlines captain. "However, in this case, because the captain had not been drinking, Delta made the right decision by asking her to leave the plane."

Aimer explains that in situations like this, flights usually end up delayed or canceled because the captain will take himself off the flight.

"It's an either you or me situation," said Aimer. "She had to go because the captain has his crew and hundreds of other passengers to think about."

Aimer adds that if he found himself in a similar situation, he'd do the same thing.