What I was thought was bizarre and interesting was how the game introduces the player to Terra first. Naturally, the player would think Terra is the main character surrounded by some equally important secondary characters. However, once the huge plot twist hits, you're in control of Celes and Terra becomes an optional pick-up of sorts. I don't think there's a single other FF game where the first playable character isn't the main one.

EDIT: FFXII! Although way different in structure than VI, XII starts you off with Reks instead of Vaan.