Why does mirror lies sometimes?

Problem

Imagine you are standing in front of a mirror, facing it. Raise your left hand. Raise your right hand. Look at your reflection. When you raise your left hand your reflection raises what appears to be his right hand. But when you tilt your head up, your reflection does too, and does not appear to tilt his/her head down. Why is it that the mirror appears to reverse left and right, but not up and down?

Solution

The definition of left and right depends on the observer and is reversed when facing the opposite direction. The definition of up and down does not depend on the orientation of the observer. 

Well, I don’t think, its because humans are left-right symmetric and not top-down!!!

Just stand in front of a concave mirror (or might be the convex - I don’t remember, which exactly. Been some time, since I’ve read this physics) beyond the focal length and try the same excercise - one would obviously find the top-down symmetry also coming into play.

I think, the reason is that flat-mirrors’ focal length is infinity and we always stand within its focal lenght and don’t see the image inverted.

Correct me, if I’m wrong!