As I understand it, the blue field on the flag is always supposed to face “forward”...so the flag on their right sleeve is inverted, with the blue field on the right, toward the front of their bodies. You’ll see the same thing if you look on a commercial airliner and they have the American flag in front of the registration near the tail. The blue field is toward the front of the aircraft, regardless of side, so the flags on the right side are reversed with the blue on the right.
I’m not in the military, so there maybe another reason.
}:-)4
The blue field is placed that way, so the flag seems to fly freely. Imagine if a flag were flying on a jeep. The blue field would be on the left or right depending on the side of the car you were on.