A mirror reverses front and back. Because we are (more or less) horizontally symmetrical, we reduce the discrepancy by rotating the image around a vertical axis

A mirror reverses front and back. Because we are (more or less) horizontally symmetrical, we reduce the discrepancy by rotating the image around a vertical axis, resulting in a left-right reversal. If we were vertically symmetrical we would see mirrors as reversing up and down; if we were front-back symmetrical (a pushmi-pullyu) we would see mirrors as they are.