Why is the U.S. Flag patch backwards on military uniforms?

The U.S. flag patch on military uniforms often appears "backwards" because it is oriented to simulate how the flag would look if carried into battle. The stars (union) are positioned toward the front, as if the flag were flying while moving forward. This aligns with flag protocol, where the union is always to the flag's own right (viewer's left) when displayed. On the right shoulder, this results in a reversed appearance. The Army and Air Force follow this convention, while the Navy and Marine Corps may use different orientations based on their traditions.

The flag is only reversed on the right side of the uniform.

Army Regulation 670-1, Wear and Appearance of Army Uniforms and Insignia.

Regulation 670-1 states that when authorized for application to the proper uniform the American flag patch is to be worn, right or left shoulder, so that the star field faces forward, or to the flags own right. When worn in this manner, the flag is facing to the observers 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.