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