The future society of the novel is based on collective thinking, as promoted by the enormous television screens that make up entire walls of houses. Because everyone thinks what they are told to think by the government, the power of individualism is a great danger to the government's power; books, with their enormous range of ideas and concepts, are a physical representation of individualism. When Montag becomes obsessed with books, he loses the trust in the collective and becomes able to think for himself; his rejection of societal values is dangerous because of his high status, and he is hunted by the government rather than be allowed to influence others.
In Fahrenheit 451, individualism is perceived as a threat to society. To see an example of this in action, take a look at the character of Clarisse McClellan. She epitomizes individuality: she is carefree and interested in the world around her. As a result, she and her family are placed under surveillance by the state. It is very clear, then, that they are considered to be a danger to society because they do not follow social norms and values.
Similarly, in Part Three, look at how eagerly the state pursues Montag. Once Montag is known to be a reader and supporter of books, the state employs every resource necessary to hunt him down bring him to justice. The Mechanical Hound, for instance, chases Montag through the city, and the hunt is televised on the parlor walls. This is perhaps because the state wants to discourage others from pursuing an individual agenda.
Moreover, it does not matter that the real Montag escapes the city. The execution of another man (who the state claims to be Montag) is enough to show that the state will punish individuality without any hesitation and with extreme violence.