Are you saying the fifty stars are towards his back or towards his front? So that if they were standing in front of you and facing 90 degrees perpendicular to you so that you were looking at their right shoulder, the patch on that shoulder would have the star field in the upper left hand corner instead of the upper right? According to American military code, the correct way is for the star field to be in the upper right hand corner, which makes it look backward to how we usually see the flag:
Eddie or Matt might have more authority on the story behind it, but the story I heard was that it's a throwback to the days where you had a guy at the front of the ranks physically holding a big flag, literally the standard bearer that lets everyone else know, "Hey, we're running towards the enemy now! Follow me!" Because he'd be running forward, the wind would push the flag back so the starfield would be in the upper right corner. If it were in the upper left, that would mean that the guy was running backwards. In other words, retreating. And since America Fuck Yeah that doesn't ever happen, it has passed down the generations to end up on our soldier boys' shoulders as such.