Vonnegut's opening line, is prophetic in its satire: "The year was 2081, and everybody was finally equal." The culture of Bergeron's society values mediocrity so much that people accept stringent and oppressive measures in the name of equality. For instance, the compliant Hazel Bergeron praises the incompetent announcer on the television network who is unable to even say "Ladies and gentlemen":
"That's all right--....he tried. That's the big thing. He tried to do the best he could...He should get a nice raise for trying so hard."
In light of the No Child Left Behind Law of 2001, Vonnegut's warning was not without foundation. Rather than heed his warnings, however, educational bureaucracies have brought to fruition the problems Vonnegut foresaw in making people forcibly the same. Interestingly, all the attempts to pull up people through educational laws, quota systems, points for certain groups, etc. have all failed to provide any real equality.
With the social movements of his time and the advancement of technology, Vonnegut foresaw a society of artificiality, mediocrity, and compliance with a large government that dominates personal lives. His story is a warning about the end of the liberty of the individual.
Vonnegut points out various concerns he has with the American culture of the early 1960's (the story was first published in 1961) through "Harrison Bergeron." Beyond all of the specific problems he highlights, he is calling for people to think for themselves and to rationally evaluate situations and societies, instead of blindly accepting whatever the leaders proclaim.
Vonnegut is pointing out the fallacy of legislating equality. In the 1960's, the Civil Rights movement was at its height in the United States. Vonnegut cautions that, carried to the most extreme extent, people who are made "equal every which way" through amendments and laws and handicapping devices will end up loosing their individual freedoms and rights. He suggests that personal liberty is more important than everyone being equal to everyone else.
Vonnegut is issuing a warning that society needs to be aware of organizations becoming too powerful. The Office of the Handicapper General seems to have taken over control, not just of monitoring equality, but the functions of all individuals in all stations of life. In a different way but with an equally harmful impact, the mass media (as represented by the television in the story) has come to dominate peoples' thought processes to the point of rendering them incapable of thinking for themselves with any independence or originality.
Vonnegut is challenging his readers to be aware of preserving individual rights and liberties, not surrendering to societal influences that might deprive people of their individual freedoms.