Why do mirrors reflect text horizontally but not vertically?
Is there a simple explanation for this?
Because you are confusing relative and cardinal axes of direction. If you stand in front of a mirror and point up, your image points up. If you point left, your image points right. However, up is relative to the surface of the earth, and left is relative to you. If you were to point left as well as east, your image would point east too - now you are considering direction along a common two dimensional set of axes, relative to the earth. The real brainfuck occurs when you point toward or away from the mirror, because now your image points north when you point south, and vice versa - however, other comments here have a much better explanation for that than I can muster.
Think in terms of projections. Take a piece of paper. Poke holes in it to make the word “TEXT.” Face the front of it to the mirror - it’s reversed in the reflection, but in a way that matches the backside of the paper. Hole for hole, they are projecting onto the mirror surface. What you see is the result of that.
The mirror reflects, but your brain interprets it as a 180° rotation around an axis in the plane of the mirror, perpendicular to the line between your eyes.
The mismatch reverses the text.
Because you rotated around the vertical axis to look at the mirror. If you did a headstand to face the mirror it would look upside down.