The premise of Vonnegut's short story "Harrison Bergeron" is society cannot be successful when trying to create equality by stripping individuality from its people.
In the short story the government tries to give people who are above average intelligence, strength, or beauty "handicaps" in order to give the illusion of equality. For example, Harrison's father George is given a "little mental handicap radio in his ear" because "his intelligence was way above normal." This radio transmits a "sharp noise to keep people like George from taking unfair advantage of their brains." People must not remove their handicaps, or they will be punished.
Despite the government's efforts, it is evident the system of handicapping individuals does not work. A prime example of this is the dynamic between George and Hazel (Harrison's parents). While watching television, Hazel is aware that George's transmitter is emitting a sound as she watches him "wince." Although she does not have to wear a handicap, she deals with the emotional burden of watching her husband suffer from having his. She wants her husband to have some respite from the pain the transmitter inflicts on him. She tells him to rest because she "[doesn't] care if [George is] not equal to [her] for a while.” This dialogue indicates that the government's attempts to make people behave and appear as equals does not have an impact on their interactions with one another. Basically, the handicaps are not causing the effect that the government hopes because people still recognize that they are not equal.
This is further illustrated through the narration of the story. The narrator describes the characters in relation to their handicaps. By doing so, this focuses the reader's attention to the handicaps and what they mask, rather than how the characters are now equal as a result of the handicaps. An example of this is when George and Hazel watch the ballet. The narrator describes the dancers in terms of their handicaps and how the handicaps reveal how talented or beautiful they really are. As they dance, the ballerinas "were burdened with sash weights and bags of birdshot, and their faces were masked, so that no one, seeing a free and graceful gesture or a pretty face." Rather than detracting from their beauty and talent, the handicaps emphasize and draw attention to their above average qualities.