//There,s nothing deep about what you see in a mirror, what you see is what anyone sees who stands in front of you, your right arm to an observer appears on their left.//
Whereas if the observer is you, your right arm appears to be to your right, unless . . . you're standing before a double mirror, two mirrors aligned vertically at right angles to each other, then you appear to yourself orientated as others see you when standing directly in front of you, which by the way is the reason such mirrors are so arranged . . . if not in an attempt to shake your own right hand.