When one looks into a mirror, one see an image of himself....
When raising one's right hand, the image raises its left. When raising one's left, the image raises its right.
So, why is it that the mirror reverses left and right, but not top and bottom?
Why does a mirror appear to invert the left-right directions, but not up-down?
The directions "up, down, east, west, north, south are fixed with relationship to the local surface of the earth. So if you raised the eastern hand, then so would the reflection.
Left and right are relative to the person/image. Similar to clockwise, counterclockwise. Since the image is rotated 180 degrees along the vertical plane, the relative directions of left/right also rotate.