Why was symmetry invented?

Answer 1

Symmetry was not invented by man in the same way electricity, air, the concept of two, the ocean, a spiral, a circle, or movement were not invented by man.

It is an observation of a natural (and man-made) pattern often seen.

Since it's an observation (a description, if you will) it was not invented. As to a reasoning behind the observation, there most likely was none; it was simply observed and noted at some point in history.