This may seem obvious at first… because, well, its a mirror image. But the real question isn’t so much why does a mirror reverse an image left to right, but WHY doesn’t it also reverse it vertically?
Think about it… If my left and right are switched, why aren’t my head and feet?
Doper physicists, enlighten me.
It doesn’t reverse left to right. It reverses front to back.
And why should be obvious.
There is no reversal of the image. It seems that way to you because when YOU turn around, YOU are reversed left to right. If you were in the habit of turning around by flipping onto your hands, then you would think the image had “reversed” top to bottom.
Cecil has written a column about this, but I couldn’t find it by searching the archive. It’s in one of the books. Time to get the archive updated?
Take a piece of clear plastic, and wwite something on it, and then stand in front of a mirror. You can read the words through the plastic. The mirror won’t reverse them.
What Faldage said.
Trinopus
This is one of those things that I have never been able to fathom.
No, not why mirrors reverse things, but why people seem to think that a mirror “swaps left and right, but not up and down”, when it clearly doesn’t.
Stand in front of a mirror. Point towards one of the side walls of the room, say the one to your right.
Which wall is your reflection pointing at?
Yes, the same one that you are.
I tried the experiment and the guy in the mirror gave me the finger. You think the mirror is faulty? Should I return it? 
Perhaps it’s the buck teeth, the mouth breathing and the Alfalfa hairdo…
Well, mirrors obviously invert your chirality.
It’s not left/right/front/back that’s flipped. It’s COUNTERCLOCKWISE-ED-NESS that gets changed.
Screws from the world inside the mirror won’t thread onto our world’s nuts! ahem. If you could grab and eat that food in the mirror, it would have little nutrition (if not being outright poisonous.) For this reason, if you ever wind up on the wrong side of the looking-glass, it’s critically imporant that you not lick anything.
Hm. What happens if you hold your faulty mirror up in front of a second mirror, forming an infinite tunnel? Will each sequential reflection hold a copy of yourself who performs multiply-unseemly behavior?
Because all the amino acids we’re made of are left handed and the ones in the mirror are right handed, true?
Not to mention that sometimes the same amino acid tastes bitter or sweet depending on whether it’s the left or right form.