Another example: Suppose you are holding a book vertically in front of you. You want to see how it looks in the mirror, so you flip it to make it face the mirror. If *you* flip it left to right, the mirror image will be reversed left to right. If *you* flip it top to bottom, the mirror image will be reversed top to bottom.

Suppose, instead you have a text printed on a transparent sheet, so you can view it in the mirror without rotating it. Then there is no reversal of the text (except front to back, which doesn't matter).

We say that our own images are reversed from left to right because that corresponds to the (approximate) symmetry of the human body. It is less odd to say "The guy in the mirror is left-handed" than to say "The guy in the mirror has his face on the back of his head".