It isn't symmetrical, your eyes are just not up to the task of seeing the infinite fractal cat along the edge leading to an infinitesimal singularity at the edge of spacetime.
when an embyo forms, the sides of the face form separately and grow together in the center. That why you have that 'snot ridge' under your nose, and if it doesn't meet up right you end up with a cleft palette and hare lips.