You will notice that all our apparel has an advancing flag on the right sleeve, unless a flag is the subject of the design. First, being on the right sleeve represents "The Place of Honor".
Second, the idea behind the backwards flag is to make it look as though the flag is in the breeze as the person wearing it 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 flag into battle.
As this standard bearer charged, his forward momentum caused the flag to stream back. Since the Stars and Strips are mounted with the canton closest to the pole, that section of the flag stayed to the right, while the stripes flew to the left.