In order to understand this thing, we need a flashback.
The year now is 1991, Square USA have relatively recently released the localised version of Final Fantasy, and are beavering away on localising the sequel, but wait, what's this? A wild SNES appeared!
The release of the SNES was a crucial branchpoint in history. Square could continue to release the NES games, thereby locking themselves to the old hardware, or they could down tools and start work on the latest Japanese release, the much prettier Final Fantasy IV. They opted to do the latter and, recognising that Americans are easily confused by nonsequential numbers and difficult gameplay, dumbed the whole thing down considerably and renamed it Final Fantasy II.
When the time came to do Final Fantasy VI, (V having been considered too fiddly for yanks), Ted Woolsey was in charge, and that meant there were no rules about what things ended up being called or how the dialogue was written, so this one was called Final Fantasy III.
It wasn't until Final Fantasy VII that it was generally accepted that people would realise that the reason that the numbers had jumped was that some games had skipped localisation and the actual title was used (plus they probably couldn't be bothered to rerender the opening CGI with a new title graphic).