The quote is important because Beatty knows that Montag is guilty and he is telling him he knows.
Beatty is quoting because he knows that Montag is guilty of stealing and reading books, and he is slowly building a case against him. He does it paradoxically, by quoting authors that no one in the society is allowed to read! The quotes at the poker game are Beatty's way of showing Montag that he is on to him.
The context of this quote is when Faber is communicating with Montag through the Seashell radios. Montag is sitting in card game with Beatty and some of the other men at the firehouse, and he feels guilty and nervous because he has stolen a book.
In Beatty's sight, Montag felt the guilt of his hands. His fingers were like ferrets that had done some evil and now never rested, always stirred and picked and hid in pockets, moving from under Beatty's alcohol-flame stare. (Part II)
Beatty, the paradoxical fire captain, continuously quotes at Montag. Montag is nervous enough, even washing his hands repeatedly so that he has to leave the table and return to it. When he returns, Beatty hits him with a string of quotes, saying “the sheep returns to the fold” and pointing out that all sheep stray sometimes. He is pointing out that even though Montag had doubts about his job as a firemen, he is here.
The purpose of these quotes are to show that he knows Montag stole the book, and he has him cornered. He wants to watch Montag squirm, but he also wants to prove that he is right about the society without books being better. Ironically and paradoxically, he does it through quoting literature and philosophy.
In impressive the string of quotes, Beatty quotes Sir Philip Sidney first.
They are never alone that are accompanied with noble thoughts, we've shouted to ourselves. `Sweet food of sweetly uttered knowledge,' Sir Philip Sidney said. (Part II)
This is kind of an interesting quote to start with, because Montag has a secret book. Beatty is saying that we benefit from our knowledge, and from sharing it. This is significant, because Montag is desperate to find out what is in the books. He was also curious about why a woman would decide to go up in flames with her books.
Beatty knows this. He gave Montag a lecture about the noble purpose of the fireman and the pointless nature of books when Montag stayed home “sick” after stealing the book. Of course he realizes that Montag’s crisis of faith is not at an end. When he asks Montag what he thinks, and Montag says he does not know, he is testing him and enjoying watching him squirm.
Faber’s purpose is to guide Montag through this test. It is a very dangerous time for Montag. He is still within the enemy camp, so to speak. Beatty is throwing quotes at him about the importance or danger of knowledge. Montag is nervous and overwhelmed. Faber tells Montag not to listen to Beatty because he is trying to confuse him.
Faber tells Montag to take in Beatty’s case, and let him tell his side later. In the end, it matters not. They get called to a “special case” and it turns out to be Montag’s house. He has no choice but to defend himself by turning his flame on Beatty. Then, he runs.
One of the most interesting characters in the book is Beatty. He seems widely read in a society where books are not allowed. He evangelizes the role of the fireman, but obviously loves to quote. He can also play both sides of a debate very well, so he is a man that loves knowledge in a society that appears to demean it. The paradox of Beatty is the author's way of showing that this society cannot survive. Knowledge always finds a way. It's addicting.