Comes from the word "hick" and the store "Abercrombie and Fitch." It refers to upper middle class suburbia kids who claim to be redneck, country, or white trash, but own pricey and flashy pick up trucks, wear brand name clothes like Abercrombie and Fitch flannels or Timberland boots, and collect expensive hunting equipment with no knowledge on how to use it. Fitch hicks are popular in high schools in suburban towns where you have to drive at least 15 minutes to be anywhere near a country area or even decent hunting woods.
Person 1: "Hey, why is Frank saying he's white trash? Don't his parents make bank selling insurance?"
Person 2: "Oh, yeah, he's going through his Fitch hick phase. Just wait 'till he pulls into the parking lot in a brand new $45,000 truck. You know, to prove how country he is."
Person 1: "Yeah, his L.L. Bean camouflage jacket really goes well with his nicely styled faux hawk and his $400 class ring."