Do mirrors really make images that are right left flipped?

No. The proof is to stand before a mirror and to have a friend lay down in front of you facing the mirror. If you raise your left hand you may be fooled into thinking that a right-left flip has occurred. But if that is so, why is your friend's head not flipped in position with his feet? When he raises the free hand, it may appear that there is a flip, but you still appear upright.

This is a strong and extremely persistent illusion that we create in our minds. The illusion is based on a simple and obvious fact: our BODIES are right-left symmetrical to a very high degree, but they are NOT up-down symmetrical. Why would a mirror not reflect back this basic symmetry? What you see reflected back when you lift a hand is the mirror image of the hand you raised. Another perspective would be to see your reflection as an image 'from behind', something a little like those concave sculptures that make it appear that a face is following you as you pass.