Why does the Handicapper General require different people to wear different kinds of handicaps?

To figure out why the Handicapper General requires different people to wear different kinds of handicaps, you need to remember her role of ensuring that no one is "smarter," "better looking," "stronger," or "quicker" than anyone else (paragraph 1).
With this in mind, you should review the reason why George, who has above average intelligence, must keep a "mental handicap radio" in his ear. You should compare this reason to the purpose for having the pretty, graceful ballerinas wear masks, sash weights, and bags of bird shot. You may also want to reread the description of Harrison Bergeron's police photograph and identify the "equalizing" function of each handicap Harrison wears (e.g., scrap metal to cancel out his superior strength, black caps to hide his attractive teeth).
Matching each handicap in the story with the mental or physical advantage it offsets may help you understand why different people wear different handicaps.
https://www.christenseninstitute.org/blog/the-united-states-handicapper-general/