"Harrison Bergeron" is open to interpretation as to the aim of its satire. Some believe it to be a straightforward dystopian story, with the individual oppressed and eventually crushed by the collective. Others believe it to be a satire on exactly that sort of story, with a ludicrously overpowered hero and an equally ludicrous dystopian government. In either case, most of the satire is aimed directly at government, with politicians taking egalitarianism to incredible extremes, and forcing "equality" on everyone through lowering standards.
"If I tried to get away with it," said George, "then other people'd get away with it -- and pretty soon we'd be right back to the dark ages again, with everybody competing against everybody else. You wouldn't like that, would you?"
"I'd hate it," said Hazel.
"There you are," said George. The minute people start cheating on laws, what do you think happens to society?"
(Vonnegut, "Harrison Bergeron," tnellen.com)
Of course, "cheating on laws" usually refers to cheating and breaking rational laws, not the insane laws of the story. The government here believes that it can erase jealousy, envy, shame, and resentment through elimination of exceptionalism -- similar themes are seen in Bradbury's Fahrenheit 451. However, the actual result is stagnation of culture and society, as nobody can have new ideas. Essentially, the story is a satire on freedom (individualism) versus enslavement (collectivism), although the actual satire is up for grabs.