Many sharp-eyed civilians have noted an apparent oddity on the uniform sleeves of American soldiers: backward flag patches. Why is Old Glory flipped around like that?
Only the flag patches affixed to right shoulders of uniforms are reversed, so the blue field of stars faces forward. (Left shoulder patches aren't a problem, as the stars face forward without meddling.) The reversal was inspired by the age-old practice of carrying flags into battle. When fastened to a standard, the American flag's blue-and-white portion is always closest to the pole. A flag bearer rushing into the fray, then, would naturally lead with the stars. In fact, it would be virtually impossible to lead with the stripes—the flag would simply wilt and wrap around the pole, rather than waving triumphantly in the wind.
For a soldier to lead with shoulder-borne stripes, then, might smack of cowardice and retreat, as if the toter were backpedaling away from the conflict. The official Army guidelines on the donning of flag patches add that the forward-facing stars give "the effect of the flag flying in the breeze as the wearer moves forward." So perhaps it's best to think of every soldier as a latter-day flag bearer, leading the headlong charge into battle.
It should also be noted that military flag patches are often trimmed with gold borders. This is in imitation of the gold-fringed flag, also known as the U.S. military flag. According to an executive order signed by President Dwight D. Eisenhower in 1959, the gold-fringed flag (and, by extension, patch-sized replicas) are to be used exclusively by the armed forces. That order isn't always obeyed, however; many federal courtrooms now feature gold-fringed flags, despite the fact that they should only appear during courts-martial.
Thanks to Brad Cowell for asking the question.