Petrow wrote that the man had verbatim detail of a long email, which he repeated back to him.
He told the MailOnline that he was "really shocked and couldn't believe this could happen".
"I think my face really fell to the floor in the terminal because very quickly he was reiterating to me in great detail what I had written in my emails," he said.
American Airline's wi-fi service is provided by Gogo, which is the biggest on-board wi-fi provider in the US.
Its clients include Air Canada, Japan Airlines, United Airlines and Virgin Atlantic.
Andrew Ferguson, editor at London-based thinkbroadband.com, told the MailOnline that in-flight wifi was similar to a public hotspot and should not be considered private.
"This problem is something not unique to just in-flight wi-fi, but to any public wi-fi network that is not encrypted," he said.
- nzherald.co.nz