Mirrors do not actually take the left side of the world and move it to the right.
They reflect light back toward you according to the laws of reflection. The strange left-right effect comes from the way we compare ourselves with the image.
Raise your right hand and watch carefully
Stand in front of a mirror and raise your right hand.
The reflected hand appears directly opposite your right hand. It has not moved to the other side of the mirror.
Your right side remains on the same side of the room.
The confusion starts because we imagine the reflection as another person facing us.
To stand where that imagined person appears to stand, you picture yourself turning around. Turning around swaps which side appears on your left and right.
The mirror never performed that turn.
You did it in your head.
What direction does a mirror actually reverse?
A plane mirror reverses the direction perpendicular to its surface.
If you are standing three feet in front of the mirror, your image appears three feet behind it.
Points extending toward the mirror appear to extend away behind the mirror.
People sometimes describe this as a front-back reversal rather than a left-right reversal.
That is closer to what the geometry is doing.
Why does writing look backward?
Write a word on a transparent sheet and face it toward a mirror.
The mirror reflects the side facing it. When you compare that reflection with the way the word looks after physically turning the page around to face another person, the difference appears as reversed letter order and orientation.
Again, the important operation is the imagined rotation.
A mirror reflects. It does not pick letters up and shuffle them.
Why does a mirror not flip top and bottom?
For the same reason it does not truly flip left and right.
Your head remains above your feet in the image because light from your head reaches the corresponding upper part of the mirror and reflects to your eyes. Light from your feet follows its own path lower down.
Nothing in ordinary reflection tells the image to rotate vertically.
If humans commonly greeted each other by doing front flips instead of turning around, we might spend our lives complaining that mirrors reverse up and down.
Fortunately, social customs took another path.
Why do selfies sometimes look strange when flipped?
Faces are not perfectly symmetrical, and you are extremely familiar with your mirror image.
A photograph may show the orientation other people usually see instead. Small differences in eyebrow height, hair direction, smile shape, or facial structure can suddenly look odd simply because the image is unfamiliar.
Some phone apps also preview a mirrored image and then save an unmirrored version, making the switch especially noticeable.
Is the image really behind the mirror?
No physical person or object is behind the glass.
Your brain traces the reflected light backward in straight lines and interprets it as coming from points behind the mirror. That apparent source is called a virtual image.
The image has a location your visual system can describe even though no light is actually originating from a miniature duplicate world behind the wall.
So mirrors are not performing a secret horizontal flip.
They reflect light back from front to back.
Our habit of mentally turning around to compare ourselves with the reflection creates most of the famous left-right mystery.
The mirror, for once, is innocent.
A related explanation is Why does a straw look bent in water?, which looks at another familiar effect from the same general system.
And that’s the short explanation.
Related explanations: Why does a straw look bent in water? and Why does your recorded voice sound weird?