
It's the most elegant mental trap in the bathroom. You raise your right hand, your reflection seems to raise its left, and your T-shirt reads backwards. It seems obvious the mirror swaps the sides. But it doesn't.
What the mirror really flips is depth: the axis running from you towards the glass. What was in front ends up behind. Your reflection isn't turned around as if another person were facing you; it's pressed backwards, like a glove turned inside out.
The 'left and right' is something you add. To compare your body with the reflection, you imagine spinning yourself around to stand in its place, and that imaginary turn is what confuses the sides. If you lay down instead, you'd swear the mirror flips up and down. The mirror always does the same thing. It's us who keep turning it around in our heads.