Our flag is not backwards. In respect to our symbol of freedom, patches worn on the right shoulder should always be reversed. The reason has to do with proper display of our flag.
The field of stars should always be in the highest position of honor. When viewing the flag on a wall, the highest position of honor is the upper left when displayed horizontally, and at the top (upper left) when displayed vertically. When displayed on a moving object like a person or vehicle, the highest position of honor is the front, and not the rear; so the field should be displayed to the front.
In application, flag patches worn on uniforms, the same principle applies: the star field always faces towards the front, with the stripes behind. Think of the flag, not as a patch, but as a loose flag attached to the soldier's arm like a flag pole. As the soldier moves forward, the stripes will flow to the back. If the flag were not reversed on the right, the soldier might appear to be moving backwards or retreating.
Inspired by military morale patches born out of the Vietnam conflict, our patches are designed to mount on the Velcro® of our apparel and equipment.