Books are burned in Fahrenheit 451 because they provide too much information which leads to people developing their own ideas on a variety of subjects. This creates inequality where some people are smarter than others. In this society, there is an active effort to achieve sameness among all people.
So books are destroyed because they are mechanisms that creates inequality. The idea is to focus people's attention onto one form of communication through the media of television, which is controlled by the authorities who encourage a life filled with ignorance and pleasure, watching television on huge screens that make you feel like you are part of the shows you watch.
Individual freedom is not permitted. Individual freedom is not an option, anyone who tries to resist the process is marked and hunted down. The only freedom that is openly expressed in this book is the choice of death, for example, when the old woman chooses to die along with her stash of books, and even Captain Beatty's death which he longed for to escape the empty existence of his life.
Individual freedom is a rare and precious gift, one that America fought a revolution to gain. Governments constantly try to curb individual freedom by over taxation which forces the individual to surrender his property, his salary, to a intrusive government who takes away the money of hardworking individuals to spread that money around to people who don't work.
Individual freedom is limited by governments that control the health care system, deciding who is eligible to receive life saving treatments for horrible diseases. People are forced by over taxation to surrender more and more choices in life, all this is suggested in the name of the common good.
Ray Bradbury wrote Fahrenheit 451 in response to the conditions that existed in the 1950s where is appeared that freedom was going to be limited and individual expression was going to be suppressed.
"Of the hundreds of stories Ray Bradbury has written, none are better known than Fahrenheit 451. Published in 1953 during the Cold War and McCarthy Eras, the novel reflects Bradbury's concerns about censorship and conformity during a period when free expression of ideas could lead to social and economic ostracization."
Whenever a government demands conformity of its citizens, individual liberty is curtailed, stolen and denied.