Why does the government handicap George and not Hazel?

The government in Kurt Vonnegut’s “Harrison Bergeron” attempts to create, not only an equal society, but one with no differences between its citizens. This goal is achieved primarily through the Handicapper General’s agency. In an attempt to create this uniformity among people, the HG masks attractive people (so average-looking citizens won’t feel unequal), weights athletes down (so they move like typical people), and transmits loud, painful sounds through microphones, placed in the ears of people with above-average intelligence.
To this end, Harrison Bergeron’s father, George, is required to wear an earpiece which emits these annoying sounds in his ears every 20 seconds, thus interrupting any thoughts he may be having. In contrast, Hazel is of average intelligence, often failing to recall recent events or comprehend deeper thoughts. The reader sees the unfortunate result of George’s earpiece when he briefly responds to his son’s murder, then completely forgets about it after the microphone screeches in his ear.

In order to have a completely uniform society where every citizen is equal in all facets of life, the government requires intelligent, beautiful, and athletic individuals to wear cumbersome handicaps that oppress their advanced abilities or disguise their appearances. Harrison Bergeron's father, George, has above average intelligence and is required to wear a tiny mental handicap radio in his ear. Every twenty seconds, the mental handicap radio blasts loud, annoying sounds in George's ear to interrupt his thoughts and prevent him from thinking for an extended period of time. The mental handicap radio severely impairs George's ability to think and is extremely painful. In contrast, Hazel was born with average intelligence, which means that she can only think of things in short bursts and is not required to wear a mental handicap. Her ability to focus and think deeply is extremely limited, which is why she cannot recall witnessing the tragic death of her son on the television screen.