When you look at a mirror, and raise your right arm, your image on the other side of the mirror appears to raise it left arm !
I some popular science books it is even written that a mirror switched between right and left.
If this was the case, than some very strange things would happened.
As can be seen from the applet, the image of a point on the body, which is further away from the mirror, is created further away from the mirror on the other side.
Thus, the image in the mirror is a reverse image (backward - forward) of the object.
It so happened that the reverse image of a human object is the same as the left - right reversal, due to the symmetry of the human body.