The citizenry of America in 2081 have been made equal in order to take away their civil rights, desensitize them, and control them.
By not allowing a person to be superior to anyone else, mediocrity reigns. If no one is superior to anyone else, then conflict is reduced, if not eliminated. There is, then, no challenging of ideas, no rebellion. There is no threat from anyone because society has no people who are bright and creative, and who can challenge mediocrity.
When, for instance, George Bergeron watches television with his wife and there are ballerinas dancing, he realizes that they are mediocre and he "was toying with the vague notion that maybe dancers shouldn't be handicapped." But this idea is quickly obliterated by a noise in his ear radio that drowns out his thoughts. It is only the rebellious Harrison, who breaks out of prison and frees himself from his handicaps, who challenges this enforced mediocrity. But, he is quickly killed.
When it is announced over the television that Harrison has escaped prison, the announcer says, "Harrison...is a genius and an athlete, is underhandicapped, and should be regarded as extremely dangerous." Calling him "dangerous" clearly underscores the point that the Handicapper General forcibly controls the members of society. By forcibly controlling people with handicaps, the society of Diana Moon Glampers, Handicapper General, hopes to maintain peace by limiting people's thoughts and their physical abilities.