After reading "Harrison Bergeron" by Kurt Vonnegut, George says, "pretty soon, we'd be right back to the dark ages again, with everybody competing against everybody else." Why is he comparing competition with the dark ages?

Because in an extremely competitive society only the talented and privileged succeed, whereas the less talented individuals don't have the same success. The less successful people will never live their life to the fullest or be able to survive properly. Often darkness is associated with sadness and as more people fail than succeed, more people will 'experience' darkness.