A mirror does not physically choose left and right to reverse. A plane mirror maps points in front of the mirror to corresponding positions behind it, so the true reversal is along the direction perpendicular to the mirror—often described as front-to-back. The left-right effect comes from how we mentally compare the reflection with a person who has turned around to face us.
Stand in front of a flat mirror and raise your right hand. The image appears to raise the hand on your left side, which makes it natural to say the mirror swapped left and right. But notice what the mirror actually preserves: the top of your head remains at the top, your right hand stays on the same side of the mirror as your right hand, and an object one foot to your right appears one foot to the right in the reflected scene.
The coordinate that changes is the one pointing toward and away from the mirror. If your nose is 30 centimeters in front of the glass, its virtual image appears about 30 centimeters behind it. Points farther from the mirror appear correspondingly farther behind it. In that geometric sense, the reflection flips the front-back direction relative to the mirror’s plane; it does not apply a special rule that exchanges the labels “left” and “right.”
The confusion becomes clearer if you compare a mirror image with another person facing you. To stand in your position and then face you, that imaginary person would have to rotate around a vertical axis. That rotation swaps which side appears on your left and right, while head and feet stay in their usual vertical order. We often make that mental rotation automatically, then attribute the apparent swap to the mirror.
You can expose the same idea by changing the imagined rotation. Suppose you could turn yourself upside down by rotating forward over a horizontal axis. A person produced by that rotation would exchange top and bottom instead. The mirror itself has not changed; what changed is the transformation you chose when comparing your body with the image.
Writing provides another useful test. Text in a mirror looks backward because the reflected shapes are oriented as if their depth direction has been reversed. If you write a word on transparent material and turn the material around to view it from the back, you create a similar visual result through a physical rotation. Again, the familiar left-right description comes from the comparison we make, not from a mirror detecting horizontal directions.
So “mirrors reverse left and right” is a convenient description of what the image feels like, but it is not the most precise description of the optics. A plane mirror forms an upright virtual image with equal object and image distances on opposite sides of the mirror. The geometry treats horizontal and vertical directions consistently; our everyday way of imagining ourselves turned around supplies the apparent left-right swap.