How do Harrison's views put him in conflict with the government?

Harrison Bergeron is an extremely tall, intelligent, highly-talented fourteen-year-old boy, who is arrested for plotting to overthrow the government. In the year 2081, every person in America is completely equal in every possible facet of life. The 211th, 212th, and 213th Amendments to the Constitution create a completely equal society, where talented, intelligent, athletic people are forced to wear cumbersome handicaps in order to make them equal with everyone else. Harrison Bergeron opposes the government's laws and wishes to change the oppressive regulations that make everyone equal. Harrison believes that naturally gifted individuals should be allowed to excel and celebrate their talents instead of being punished for having them. His revolutionary beliefs lead to his arrest and he is forced to wear the heaviest, most cumbersome handicaps available. However, Harrison escapes from prison, hijacks a news station, and attempts to overthrow the government by claiming to be the emperor of the United States. Unfortunately, Harrison Bergeron is shot and killed by the Handicapper General, Diana Moon Glampers.

In Kurt Vonnegut's short story "Harrison Bergeron," he evokes a future version of America where equality is legally enforced. It is now written into the American Constitution, and there is an office of the "United States Handicapper General" which is responsible for enforcing this equality. Individuals who are smarter or more attractive than the norm are handicapped: they wear earpieces that make noises to distract their thinking, masks to cover their faces, and so on.
That's the context in which Harrison Bergeron acts. That context matters a lot, because that's what Harrison is acting against. Harrison's views are not well-developed or especially well-explained. They essentially boil down to two or three things. First, Harrison rejects the enforced equality. Second, he has the gifts and abilities to do so: he is extremely smart and physically powerful. Third, he declares himself emperor. He is explicitly rejecting the projected enforced legal equality.