How come words appear backward in a mirror?

In Lewis Carroll’s Through the Looking Glass , Alice (of Alice’s Adventures in Wonderland fame) discovered that a mirror was a doorway to a parallel universe, where everything is reversed—and anything might happen. While mirrors aren’t really an entry to another world, they are very curious objects.  A mirror seems to reverse left and right—making newspaper headlines and T-shirt slogans read backward, and flipping the image of your face and body. But a mirror doesn’t flip top and bottom—we don’t appear in a full-length mirror with our head at the bottom, feet and floor at the top.