Why does the government handicap George but not Hazel?
Hazel's mind could have been the prototype for what the society desires of everyone because she has the most suitable intelligence, one that is "perfectly average," the goal. Her husband, George, however, is too intelligent and is required by law to wear handicaps.
"Equality" has been made into law in Vonnegut's futuristic America by the passage of the 211th, 212th, and 213th Amendments to the Constitution. These amendments force the sacrificing of individuality, and they desensitize people, numbing in them any kind of critical thinking that might conflict with a controlling government. The best that anyone can be is mediocre, which is the safe level for the totalitarian government.
In order to ensure this requisite mediocrity, Diana Moon Glampers is appointed as the Handicap General. She enforces the three amendments and other such laws, sending to prison fourteen-year-old Harrison Bergeron, a handsome, athletic genius who is in violation of the laws of mediocrity. His father George has also been incarcerated and fined, so when Hazel suggests he remove some of the heavy bird shot he is forced to wear, he refuses out of his fear.