The best explanation that I was to find about the topic.
Mirrors do not actually flip left and right or up and down.
When you look at a scene in a mirror, you'll notice that everything on the left remains on the left, everything on the right remains on the right, everything up stays up, and everything down stays down.
The only thing that gets flipped is the direction into or out of the mirror.
Mirrors invert depth, not left and right or up and down, because they reflect light based on the principle of specular reflection. Light enters the mirror at a certain angle and bounces back out at an equivalent angle.
The reason words appear flipped in mirrors is because we typically write them on objects that we have to turn to face the mirror in order to see them.
We flip the words left and right, but we could also flip them vertically. If a word is flipped in a mirror, it would also be flipped outside the mirror, but we don't normally notice this because we can't see through solid objects without going around to the other side and turning ourselves around.