However we like to think so, the human face is not symmetrical. Even if we take into account that the left side of the face is roughly a mirror image of the right side, there are striking differences. To demonstrate that I took a photo of myself, and manipulated it into two left sides and two right sides, appropriately mirroring each half of the face.
You can do the experiment yourself or take a photo of someone else. Be sure to have the person look straight into the camera, to avoid perspective view, which distorts the image. The surface of the face should be parallel to the surface of the camera sensor (or as close as parallel as you can get). Getting further away and using the telephoto setting of your lens obviously diminishes the parallax effect.
And yes, I know I need a haircut. I promise I’ll go to the hairdresser this week.
That is all.