It doesn't.

It only flips front and back.

That’s the neat part - it doesn’t flip either. It’s your mind playing tricks on you.

Left and right, and the act of turning around are so common to you - that when you look at your reflection in the mirror, your brain expects that image to have turned around 180 degrees either left or right. Since that didn’t happen you think it’s “flipped”. But it’s not - your EXPECTATION is that it should be flipped.

Here’s another way to think about it. If it was common for us as humans to turn around by doing a handstand to look backwards - then you’d be complaining “why do mirrors flip up and down but not left and right?” But because that’s ridiculous and we don’t do that - you have no expectations that your mirror image should be standing on its head.

Trippy right? :)

Mirrors can totally reverse top-to-bottom, you just have to bend over to see it. The left-right bias is based on the way we look behind us, not any property of the mirror.

This takes a little explaining.

A rotation is a reversal through two dimensions at once.

If you turn around to look behind you, you're swapping front-and-back, AND left-and-right.

If you stand on your head, you're swapping front-and-back AND top-and-bottom.

Stand facing the way the mirror does, then turn to look into it. You have to do some kind of rotation - a two-dimension reversal - to get there. If you're a normal human, you'll twist around, swapping left-and-right as you swap back-and-front. Your left and right ear swap places, your nose and the back of your head swap places too.

But your reflection doesn't do that.

A mirror only reverses ONE dimension: front-and-back. It's the equivalent of punching your face out the back of your head: its ears are still on their original sides. You have swapped left and right in order to face in the opposite direction, but your reflection hasn't - so it's ears are on opposite sides to yours.

But you can do it the other way.

Stand with your back to the mirror, and bend over and look under your arm (or between your legs) to see your reflection, instead of twisting around.

Hold something with writing on it, and you'll see: the letters in the reflection are upside-down, but they face in the right direction.

The only reason you don't see this very often is that it's a fucking weird thing to do and nobody ever does it.

Let Dr Feynman guide you through this question.

Stand in front of the mirror and raise your right hand. In your imagination, trace the rays of light bouncing off of your hand, bouncing off the mirror, and entering your eyes. Your right hand is in front of the right half of the mirror (as you look at it) not the left half.

Your head, however, is on the top half of the mirror as you look at it, and your torso is on the lower part. The light is simply bouncing off the mirror at angles that align left, right, top and bottom relative to you.

The image of the human in the mirror appears to be raising the left hand, because your mind has re-oriented that person to assign "left" to that hand. But it's really just the image of the right hand coming relatively straight back at you. It appears to be the person's "left" hand because we think of the image as a person facing towards us. But it's not a person. It's just an image of you.

If it helps, move your right hand towards the mirror until it "touches the other guy's left hand" and then back it off. Do this a few times and it should click what's going on.

All of this assumes you are standing right side up. :0)

It doesn't. It actually flips front and back.

Well, because it doesn't flip anything. The light just bounces off, thus light from your right bounces back to your right.

Because the mirror doesn’t flip left and right; it flips front and back.

The mirror DOESN'T flip left and right. Imagine an x-axis as a horizontal line across the mirror, a y-axis as a vertical line up/down the mirror, and a z-axis as a line that comes straight out of/into the mirror.

The mirror is actually only flipping that z-axis that comes out of/into the mirror, by reflecting the light back

It reflects your image across the plane of the mirror. This isn’t physically possible with real-world objects, so your brain substitutes the closest real-world transformation that would approximate the same appearance—which is rotating bilaterally symmetric objects about their axis of symmetry. With a vertically-oriented human, that means turning around so your left is on the right and vice versa.

ITT are a bunch of bad explanations; some are ok but here's more detail:

Imagine a transparent sheet of glass with words printed on it. Hold it up so you can read it. Now stand in front of a mirror. You can read the words, both in the mirror and on the glass in front of you. Neither set of words is flipped.

Now imagine turning the glass around so the words face the mirror. As you rotate the glass 180 degrees horizontally, it flips around mirror image. Both in the glass in front of you, and in the mirror, you can now see a "mirror image" view of the text. But the mirror didn't do anything -- you did, when you chose to flip the glass around horizontally instead of vertically to face the mirror. If you'd tumbled it top over bottom to face the mirror, then the text wouldn't have flipped left and right, but it would have flipped high and low.

Your head is similar to the text, except you can't see through it. But, if you rotated yourself to face away from the mirror, and your head was transparent, someone looking at you would see a not-mirror-image face of yours, both looking at them and in the mirror from the other side. Same as the text. Nothing is flipped. When you chose to spin yourself horizontally to face the mirror, instead of doing a headstand, you chose the transformation that will led to seeing the mirror image instead of the high-and-low flipped image of your face. If you face away from the mirror, and do a handstand instead of spinning horizontally, you'll see a vertically flipped face with its left and right preserved.

Hopefully that makes sense.

I got you:

https://www.youtube.com/watch?v=8b7Kp2uBUZg

It depends on how you want to think about it. I think Action Lab did the best short video explanation of how your perception of mirrors makes things look flipped.

https://www.youtube.com/watch?v=bDpWhg-hbHo

What are you talking about?

mirror don't flip up and down nor right or left, it flips front and back. because that is how sumetry works (where the mirror is the symetry plane).

if you point right, your reflection will also point your right. same for left, up and down. but if you point forward, it will point back toward you (behind you, that is)

It's your brain that is tricked by your reflection and takes it for a real person, so when you move your left arm, your brain understands it as if your reflection moved its right arm.

Tilt your head 90 degrees to one side. Bam! Now it flips up and down.

When you face someone, why does your left and their left flipped from one another ?
Any object we face are flipped : it's true also where you are in front of a car from instance ... it doesn't happen when you are inside the car or inside yourself.
if you can see this, you can understand the mirror as well.

Because the mirror flips your eyes!

You got a left and a right eye. Now if you had a top and a bottom eye instead, then the mirror would not flip left and right, but top and bottom.

Buuut... if you had 4 eyes: left, right, top and bottom, then the mirror would flip them all!

Because it's not flipping, it's reflecting.

It's because left/right are physical relationships that are relative to YOU. Up/down are relative to the ground (ie, really, center of the earth).

Mirror images more resemble being flipped inside out. Sort of.

Imaging holding your hand out flat, parallel to the ground while facing a mirror. The tips of your fingers would be closest to the mirror.

Now imagine if you were wearing a glove on that hand and you took the glove off so it were inside out.

If you were to compare the inside out glove to the reflection of the hand the glove came from, they would look similar.

Mirrors just show us what they see.

It does. Every part of a reflection is made so that your reflection touches you. If it were upside down, it couldn't do that. If both you and your reflection raised your left hand instead of one raising their right hand, it also couldn't do that, and there would be nothing preventing you from reaching your hand in that parallel universe.

I am an aphantasiac and needed to look at the two queen of hearts in a deck of cards to realize this.

Mirror doesn't flip, camera flips.