The Legend Of Zelda: The Skyward Sword.

[Rhyme]

Maybe Link's just ambidextrious, that's why he holds his sword with either one hand or the other.

If you're referencing Twilight Princess there, it wasn't like that on purpose; they were lazy with the Wii/GC conversion and just flipped the game around (Inverted) if a doors on a left on GC, it's on the right on the Wii