Why did Captain Beatty believe books should be destroyed?
Beatty's explicit reason for destroying books is to maintain social order.
Early in the story, shortly after stealing a book from a woman's house that the firemen burn, Montag becomes sick with guilt, and considers calling in sick. He doesn't even realize that he's already late for work as he considers this, and Captain Beatty promptly arrives to "see for himself" how sick Montag is. He knows Montag isn't really sick, and Beatty is such a perceptive person that he knows Montag is experiencing a sort of moral crisis that, according to Beatty, every fireman goes through sooner or later. Beatty then describes the true history and purpose of the firemen.
According to Beatty, society got so overpopulated, so sensitive to insult, and so concerned with pleasure, that things which created divisions became so unwelcome as to be dangerous to social order itself. He gives the example of a bright young student in school; this student, by making others feel stupid, whether intentionally or not, caused unhappiness and discord. Beatty concludes;
You must understand that our civilization is so vast that we can't have our minorities upset and stirred. Ask yourself, What do we want in this country, above all? People want to be happy, isn't that right? Haven't you heard it all your life? I want to be happy, people say. Well, aren't they? Don't we keep them moving, don't we give them fun?
Beatty asserts that books are traitorous and divisive; what one person might see as valuable knowledge might offend another. He mentions that "the Devil can quote scripture for his purposes", and that books are ultimately incompatible with a society that prizes happiness and calm. He also suggests that censorship came "from the bottom", i.e. from the people, and is therefore a democratic act.
On a deeper level, Beatty is a well-read and philosophical person in his own right, and he believes there is a loneliness to the universe that society helps us to ignore. Beatty does not want to worry about this; he prefers the life of instant gratification and minimal thinking that social has fabricated.