I don't quite understand the mirror explanation. He made it sound like it's only flipped left and right because our brain trick us. But if you take a picture of you raising your left hand in the mirror, the picture will show you raising your right hand, right? That means the flipping did happen and wasn't an illusion created by the brain.
It's not an illusion like an optical illusion where your brain tricks you into seeing things, a flip is occurring just not in a way that the brain would intuitively imagine. The "illusion" is more in the way of thinking that your brain produces.
If you stand in front of a mirror and raise your left hand, your reflection's right hand raises. Intuitively this seems like a right/left flip. Like if we imagine the reflection as another person, then to go from your current position to that position you need to walk around and turn to face the other way, so we naturally think of it as a left/right flip.
As a side note, if you imagine yourself standing on top of a mirror, now it would seem like your up and down have been flipped in the reflection instead of left and right. Your feet would be at the top and your head at the bottom, but raising your left hand would still make your reflection's left hand raise.
However, what a mirror is actually doing is flipping the back and the front. But it's hard to intuitively think of the mirror as flipping the back and the front. Like a person doesn't squash into themselves so that their back goes through the front until they're facing the other direction. So the "illusion" is in thinking that a mirror flips left and right (or up and down), when in reality it's flipping front and back.