I will probably not be the first person in this debate to say that everybody else was wrong. :) The real reason is, of course, the relative symmetry of humans. We look horizontally symmetrical, that's what makes it possible to say that a reflection of our hand or face is still a hand or a face. Imagine that all humans looked like a giant @ symbol. The reflection in the mirror would look pretty weird to us then. :) The question would not be why mirrors reverse this or that, but why mirrors turn a normal human into a wicked alien creature, or actually "who is this monster behind the glass wall?" :)
The left hand in the mirror is still our left hand seen reflected. Our head is still the head seen reflected. You need to be in a really bad state to mistake your head for a pair of legs, but you can easily persuade yourself that a hand or an eye in the mirror somehow changed their affiliation.
While I believe that our findings are extremely valuable and useful, still we have only begun to uncover the mysteries of the mirrors. To stimulate further scientific inquiry into this phenomenon, I suggest several experiments that may greatly benefit human knowledge and further enhance our understanding of the psychological, logical, political, geographical or other effects of mirrors.
- check if mirrors reverse the polarity of the magnets
- investigate the claim that mirrors reverse the aging process. Some researchers suggest that mirrors actually accelerate it.
- check whether mirrors reverse North and South or East and West in terrestrial globes. What effect, if any, can be observed for globes of Moon or Mars? For a featureless white sphere? For a mirror glass ball (hold near the mirror)?
- check if mirrors reverse any latin letters or arabic numbers
- attempt to devise a text string the meaning of which will be reversed in mirror
- is it possible to achieve the same or better effect with kanji
- try to devise a mathematical theorem the reflection of which would be its own proof
- find out whether one-handed researchers observe the same effect?
- do the same for one-eyed researchers
- try to explain the problem to blind researchers (preferably those blind from birth)
- try to do the same with a deaf researcher (ask him not to look at you directly, but use a mirror instead)
- form a focus group of Siamese twins and dicsuss the problem with them. Analyse the effect that their relative positions has on their opinions. Of particular interest is the opinion of twins adjointed at their occiputs
- evaluate the feasibility of using mirrors as input devices in optical quantum computers
- is the behaviour of animals affected by the regular mirrors and angular double-mirrors that do not "reverse left and right" differently? Non-symmetric animals like certain crab species are especially interesting in this regard
Please feel free to add the results of the experiments that you perform below or suggest other ones.