Conspiracy theorists will say what they will ...
but it’s done that way, so that it will present the same appearance as if it were being flown from a staff in the Soldier’s hands. And it’s on the Soldier’s right, because that’s the position of honour.
I read somewhere that the flag used to be normal-facing (field on left) on both shoulders. One of the US Generals saw the flag on the uniform, and to him, it appeared that the soldier was running backwards when viewed from the right.
None of his soldiers would run from a fight, they would run TO the fight, always advancing forward. So the flag on the right shoulder was reversed, to indicate forward movement.
The flag on the left shoulder is field-left, also indicating forward movement.