If they won't tell you the reason, you should consider the FOIA request. Apparently there is something on your record that made the agent suspicious -- and the supervisor confirmed it. Based on your posts, it is likely a mistake of some kind that you probably want to clear up regardless before you start a lot of international travel. Based on news accounts of the No Fly list, including flagging a sitting member of Congress, there are plenty of mistakes in the government's background files.
http://www.nytimes.com/2012/10/09/bu...anted=all&_r=0
Mr. Wagner said that 3 to 5 percent of travelers were rejected, out of about 30,000 applications every month, and that individuals are generally told the reason for the denial....
Those whose Global Entry applications are denied have three ways to appeal: making an appointment to speak with a supervisor at a trusted traveler enrollment center (listed at globalentry.gov), e-mailing the agency’s ombudsman (
[email protected]) or filing a complaint through the Department of Homeland Security’s Traveler Redress Inquiry Program (dhs.gov/trip).