People often ask questions like “Why does a mirror reverse things horizontally but not vertically?” – which is odd because a mirror does not always “reverse things horizontally but not vertically”.
For example if it is lying on the ground (or is the surface of a lake) it reverses things vertically but not horizontally.
(See also this beautiful image
What a mirror always does is reverse forwards and backwards (relative to itself). So when you look into one on a wall it does reverse things horizontally – but front to back rather than side-to-side.
It also always reflects your left to the image’s right (but not yours!)
If you hold a red ball in your right hand and a green in your left, then the mirror does not reverse the direction from red to green unless you are standing sideways relative to a vertical mirror. And if you are facing the mirror the red ball in the image will still be on your right and the green on your left. But no matter how you and the mirror are oriented your image will have the red ball in its left hand and the green in its right.
The reason a mirror always reflects left into right in that sense is because left and right are not defined in their own right(*) but only by their relationship to the two perpendicular directions from feet to head and from back to front.
If you swing an arm from pointing directly forwards to overhead and continue in a clockwise motion, then the next perpendicular direction it gets to is actually the definition of “right” (and similarly, a counterclockwise swing takes us to the “left”). And since a reversal of any direction switches clockwise to counterclockwise it also switches left into right.
(*)- For example, the heart is usually left of centre in the body, but we don’t define left as “heart-side” because in the rare cases of people who are reversed we say that their hearts are on the right rather than re-defining left and right for them, and similarly people who are left handed don’t use a reversed definition of left and right when talking about the world around them.