Fashions come in and out, and beards alternate between trendy and passe. By the introduction of the safety razor, shaving had obviously become so common that even the poorest farmer could afford to walk around with smooth cheeks.
But who was the first culture to say "this stuff growing out of our faces is rubbish" and what was the reason? I know that Alexander ordered his soldiers to shave their beards, but an army is not a society, so that doesn't really count unless the folks back home emulated this shaving.