Harrison is incredibly gifted, mentally and physically. Even though he is only fourteen years old, he is seven feet tall. The job of the Handicapper General is to give people handicaps in the form of mental distractions and physical restrictions. The Handicapper General's job is to handicap those who are physically and mentally superior to others. The idea is to make everyone equal.
But Harrison is so gifted that Diana Moon Glampers, the Handicapper General, has had to give him the most oppressive and restrictive handicaps she can come up with. His physical handicaps way 300 pounds. But even these can not contain him. He is that powerful. When he storms the television studio, he sheds his handicaps with ease.
Harrison tore the straps of his handicap harness like wet tissue paper, tore straps guaranteed to support five thousand pounds. Harrison's scrap-iron handicaps crashed to the floor. Harrison thrust his thumbs under the bar of the padlock that secured his head harness. The bar snapped like celery. Harrison smashed his headphones and spectacles against the wall. He flung away his rubber-ball nose, revealed a man that would have awed Thor, the god of thunder.
Harrison's power (which, in the end goes to his head) threatens this dystopia of a society where everyone is equal. That's why he is a threat to the Handicapper General.
Harrison's outspoken demeanor and defensive actions are a direct threat to the handicapper general because people were not permitted to speak out against the law of "equality." This law, created by the handicapper general, required physical "handicaps" to be worn by all those who appeared to be "too perfect" when compared to others who were considered imperfect. In order to make everyone equal, physical handicaps included heavy weights for those who were athletic and shock collars for those who were intelligent. Harrison's so-called criminal behavior of being an activist against the handicapper general's realm not only disrupted the perfect, equal, dystopian community, but also influenced the controlled behaviors of others.