No one has a damn clue who first said "If you have two starting quarterbacks, you don't have one" — it's easier to just write it as an "adage" or a "football saying" than to do the etymological excavation, apparently — but the logic of that theory seems sound: Two quarterbacks of relatively equal caliber competing for a single job tends to not work out.
Florida's recent history bears this out, though the difficulties the Gators have had have been related not to struggles with naming a starting quarterback but the fallout from such decisions.