You know, that was exactly my answer as a teenager as well, and the answer I thought I knew when I clicked on this thread, but I don't think it's a sufficient explanation. Even if you assigned up and down as relative, no vertical flipping appears to take place.
I believe InclinedPlane's answer [1] is much better. We implicitly perceive the reflection as having rotated as a human would, by turning around on his or her feet.
However, if instead the reflection is perceived as having rotated vertically, with the human flipping over onto his or her head, the image is actually flipped vertically.
So the answer is actually that the image in the mirror is either flipped horizontally or vertically, depending on one's perception of how the mirror image got there in the first place.
While the local/global orientation explanation does show that there are no inconsistencies, and the lack of a relative orientation for 'up' clouds things a bit, it doesn't actually explain at all why we naturally look at the image and decide it's flipped horizontally.
Left and right has one frame of reference - facing. Up and down has another frame of reference - room ceiling/floor. Mirror inverses the facing frame of reference but not the room frame of reference.
Left and right, up and down are just convention in our mind. We human use facing to assign left and right, and use ceiling and floor to assign up and down. There is no switching sides in the mirror in reality. You red hand (if you color it) is on the same side inside or outside of the mirror, just as your head and feet are on the same side inside or outside of mirror.
We just assign a new left/right to the mirrored image because we see where the facing in the mirror is; however, our head is near the ceiling and feet are still on the floor so the room frame of reference hasn't changed, and thus up/down are labeled the same in the mirror.
The point my history teacher trying to make via this exercise was to say most stuffs (in history particular) were relative in a frame of reference. It's the same event but through a different angle would be called different thing, when moved to a different frame of reference. The mirror exercise is the terrorist/freedom fighter argument in physical illustration.
I believe InclinedPlane's answer [1] is much better. We implicitly perceive the reflection as having rotated as a human would, by turning around on his or her feet.
However, if instead the reflection is perceived as having rotated vertically, with the human flipping over onto his or her head, the image is actually flipped vertically.
So the answer is actually that the image in the mirror is either flipped horizontally or vertically, depending on one's perception of how the mirror image got there in the first place.
While the local/global orientation explanation does show that there are no inconsistencies, and the lack of a relative orientation for 'up' clouds things a bit, it doesn't actually explain at all why we naturally look at the image and decide it's flipped horizontally.
[1] http://news.ycombinator.com/item?id=2790792