To decide who is the fairest of them all, the mirror has to distinguish between the person looking at the mirror and the reflection in the mirror. They are not the same. The reflection is an inverted image of the person standing before the mirror.
(Actually the shift is not from the left to the right as it appears, but front to back. Click here for a detailed explanation.)
Think of the word ecnalubma on the front of an emergency vehicle in order to see the word ambulance in your rearview mirror.
In this image, the girl is wiping the mirror with her right hand but the reflection in the mirror is using the left hand.
Although the human face is symmetrical, one side similar to the other, they are different. The you you see in the mirror is not how other people see you, because there is always a difference between the two sides of the face.
Symmetry is necessary for balance and beauty. We immediately perceive when the symmetry is out of balance. A crooked picture calls our attention.
A slight variation of symmetry in the human face adds to its interest and beauty. The lip curl, difference in eye color, one cheek fleshier, eyebrows, crooked smile? If both sides were exactly the same, the face would be bland, and if way out of balance it would be grotesque.
Are we aware of this when designing a site?
The simple expedient of introducing a slight imperfection to any element of the site that is intended to be symmetrical such as background color or designs will call attention to the site. Presenting a human face and its flip on a site will convert the casual glance into a gaze.