Why mirrors reverse left and right, but not up and down (idea) by TeknoHog

Alternatively, the basic reason is that mirrors reverse front and back. Our notions of left and right describe the relation between "this side"/"that side" and front/back. On the contrary, top and bottom are independent of the front/back direction. In the mirror image, "this side" and "that side" are unchanged, just like top and bottom, but front and back are swapped, so in effect left and right are reversed.

Interestingly, a combination of two mirrors at a right angle does not reverse left/right. In addition to front/back, it reverses the sides. The net effect is like (-1)*(-1) = 1, and the notions of left/right are unchanged.

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