Today I learned something new, thanks to @Gleisplan.

When a US soldier has a US flag patch on his shoulders it looks like the flag is mirrored on his right shoulder, but that is intentional.

The idea is, the right shoulder patch looks like a real flag would look, if the soldier was carrying a real flag on a pole and running forward — if you stood to his right you would indeed see the stars of the flag to the right in the direction the pole is moving.
https://mastodon.social/@Gleisplan/115226570453958167

@randahl @Gleisplan
Have people never seen a real flag? Only pictures of flags with the wind coming from the left?

Real flags have two sides, and most if not all flags have the same part of the flag (in this case the stars) towards the flag pole on both sides.

Though I do seem to recall seeing pictures of a made in China American flag with the stars away from the flag pole on one side.