i never understood the question: how could anybody ever even think that a mirror flips left and right? there is no emperical way to observe this behaviour (with a single flat mirror).
This is one of those Feynman questions where understanding the question requires a certain way of thinking that discards common sense. Similar to his "Why is the wall not see-through?" question. The way I think about is: "When you are looking at a mirror, and you blink your left eye, mirror-you blinks his right eye. But when you are laying on your side looking at a mirror, and you blink your top eye, mirror you blink…
maybe this question would make sense, if i would see myself as the center of the universe, all creation and all there is - but there is a pretty high chance that i ain't. (and even then i'm not sure if this question would make sense)