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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 rule dates back to the Army's early history, when both mounted cavalry and infantry units would designate a standard bearer, who carried the Colors into battle. As he charged, his forward momentum caused the flag to stream back. Since the Stars and Stripes are mounted with the canton closest to the pole, that section stayed to the right, while the stripes flew to the left.