They aren’t wrong. What does a flag look like when someone is holding it and running forward aka towards the enemy?
It’s how all US flag patches are on military uniforms. Tradition from the days when there were standard bearers. Being a standard bearer was a pretty big deal, it was a huge boost to moral to kill the enemy standard bearer and many times when men would see their sides flag fall, it wasn’t long before they broke. Promotions and awards were given to men that captured an enemy unit’s flag.