Why Do Mirrors Reverse Left and Right but Not Up and Down?

Imagine you are a superhero looking in a mirror. When you raise your right hand, the person in the mirror raises their left hand (or so it seems). But wait! If you jump up, they jump up too. They do not flip upside down. Why?

Think of the mirror as a window into another room where a perfect twin lives. Your twin is facing you. To stand face-to-face with you, your twin had to turn around. When you turn around, your left hand stays on the left side of the room, and your right hand stays on the right. However, because your twin's chest is now pointing at yours, their left hand crosses over to meet your right.

If you hold up a piece of paper with writing on it to a mirror, the letters look backward. This is not because the mirror flipped them sideways like a pancake. It is because you turned the paper around to show the mirror. If you lay the paper flat on the table and lift it straight up to the mirror, the writing stays normal! The mirror only reverses front-to-back. Your brain just likes to pretend the reflection is a person standing in front of you, so it guesses a left-right swap instead.