"If you rotate the pole so that is facing you and you can now see the front of the card you see that the blue dot is really on the left and the red dot on the right.
This proves that the mirror flips left and right."
All it proves is that you've rotated the card. You've done the flipping, not the mirror.
Now, without doing any rotation to the card, if the card is seen from the perspective of the mirror, the blue dot is on the left, and the red on the right.
Depending on which perspective you're looking at an object from, one side will be on your left, and the other on your right. But no flipping takes place, unless you either move yourself to a different perspective, or rotate the object. A mirror does neither. It just reflects back exactly what's in front of it.. so you see whatever's on your right on your right, and whatever's on your left on your left. There is no flipping.
This proves that the mirror flips left and right."
All it proves is that you've rotated the card. You've done the flipping, not the mirror.
Now, without doing any rotation to the card, if the card is seen from the perspective of the mirror, the blue dot is on the left, and the red on the right.
Depending on which perspective you're looking at an object from, one side will be on your left, and the other on your right. But no flipping takes place, unless you either move yourself to a different perspective, or rotate the object. A mirror does neither. It just reflects back exactly what's in front of it.. so you see whatever's on your right on your right, and whatever's on your left on your left. There is no flipping.