There isn't really a left to right reversal at all, physically speaking - there is only a front-to-back. Then, as Will Fly explained, if you try to superimpose yourself on that reversal, the easiest way to do so is to call it a left to right reversal.

Here's a simple, if slightly insane, experiment. Put a brown paper bag on the hand of your choice, and wear a hat with a large feather sticking out the back of it (preferably one an emblem on the front). Now, stand in front of the mirror and move the bagged hand. The image moves its bagged hand. Same with the unbagged hand. There is no reversal. All that has happened is that you *want* to call the bagged hane 'left' on you and 'right' on the image. With the hat, feather and emblem you can confirm what has really changed is the front-to-back.

You can explain all of this to the nice men in the white coats ...