I thought it was so when they flipped the film for id-Kirk, he wouldn't have the insignia on the wrong side.
Until the DVD's "corrected" it, the opening shot of the planet set was flopped, with Kirk and Sulu's hair parted on the opposite sides. Kirk had no insignia and Sulu's was covered by the Space Spaniel, so we wouldn't notice. This was apparently done to make the set seem larger. Or something. The only thing to otherwise betray the trick was the writing on a box on a rock was backward. However, until the clarity of HD, we could never clearly see the label. SO now, it's flopped back, but not what was originally done back then. Just sayin'.