what explains the fact that mirrors only reverse an image left to right, not up and down?
Mirrors don't reverse either of those.
They reverse in/out. The reason it seems the left/right directions are reversed is because when we decide which hand our image is raising, we unconsciously put ourselves in its place, which involves rotating our orientation around our vertical axis so we face the same direction, undoing the in/out flip at the cost of a left/right flip (in our minds eye). We might just as easily flip about our horizontal axis and decide up/down is flipped, but since we are more or less symmetrical left to right (and also since we rarely physically perform that rotation), that is a much less natural choice.
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