Wait...did you know this about mirrors?

This video misses the problem, it doesn't solve it. The only thing it gets right is the fact that mirrors flip the Z axis. The flip of a person and the flip of the text are to completely different things. The filp of left and right hand in a person (or anything else that has a right and a left side) has to do with how right and left are established. To establish what side is the right or left you have to know an up direction or vector (which usually is indicated by the position of the head) and a front vector (which usually is indicated by the face). Without these two you cannot indicate what is left and what is right. On the other hand, to define up and down you need only one vector, not two. Then, if the mirror is in front of you, it flips the front direction, which automatically flips right and left, because the up vector stays unchanged. But if yoy stand over a horizontal mirror, then it flips the up vector and this time, both up - down and left-right change because they both depend on the up vector.