Let me un-ellipses the quote so we can make some sense of things.
> A logo should (...) have some degree of symmetry, simple enough to draw, original, and not readily resembling something in real life or a prior logo.
Symmetry is valued by us humans as a positive aesthetic.
> A logo should (...) have some degree of symmetry, simple enough to draw, original, and not readily resembling something in real life or a prior logo.
Symmetry is valued by us humans as a positive aesthetic.
Simplicity aids in recall.
Originality aids in brand recognition.
Those are some whys.