If you have seen someone in Army uniform, then you may have seen an American flag patch on their arm. It isn't too tough to imagine why they would wear a patch representing the country they fight for. The confusing thing is sometimes the patch is reversed, with the stars of the flag being at the top right instead of the left. It seems counter-intuitive, but surely the Army knows what they're doing, right?
Of course they do, and the reversed flag is no mistake. In past wars it was tradition for a member to carry a flag into battle, holding it high in the air as they rushed toward the enemy. The flag would trail behind the pole it was affixed to, making the flag appear reversed from the right perspective.
Today the flag patch is symbolic of this old practice, but instead of being held on a pole it is worn on the shoulders of uniforms. As they run forward, the flag (patch) catches the breeze and flies backward in the wind. If the flag is on the left shoulder, then it will appear normal, but on the right shoulder it must be reversed to maintain the symbology.
Army Regulation 670-1 states:
The full-color U.S. flag cloth replica is worn so that the star field faces forward, or to the flag's own right. When worn in this manner, the flag is facing to the observer's right, and gives the effect of the flag flying in the breeze as the wearer moves forward. The appropriate replica for the right shoulder sleeve is identified as the reverse side flag.