I'm inclined to believe that Beatty keeps quoting texts because at one point he has read them. I'm not sure if it is because he loves reading but still feels obligated to burn them in order to keep his job or be separated from society. It is possible that Beatty is embracing the classic "know thy enemy" mentality. He has to destroy the books. He has been told books are no good. He takes that to heart, and reads some of the books to better know why they are considered bad/evil. Being well read also allows him to constantly drop literary references to antagonize Montag. Beatty's use of literary snippets allows him to try to prove to Montag that books are confusing and contradictory. They do not offer answers, only more questions. To Beatty that is why books should be banned and burned in the first place. They serve no function, and Beatty can quote the contradictory reasons behind that opinion of his.
In my opinion, I think Beatty quotes the books because he, at some point, has become curious about the books the same way Montag has, and reads them. Beatty secretly loved the books, but he's different from Montag because he doesn't want to be separate from society and his job that requires him to burn books. During Montag and Beatty's final confrontation, it's almost set up as if Beatty wanted to die from his unhappiness and planned his own death by luring Montag to kill him. Before he dies, he even spurs out some quotes from his vast knowledge of books. It's not the most supported hypothesis out there, but it's what I think and I hope it gives you a different analysis of Beatty's paradoxical character.
There are many ways to interpret Beaty's quoting of books. Some believe that Beatty quotes the books to intimidate Montag or show that he is smart. In my opinion, I believe that Beatty quotes the books to show that he is not just every other man in the society who is ignorant and does not know the importance of knowledge. I think he wants to show Montag that he is indeed an educated man, and yet still believes that burning books is the right thing to do. He also seems to want to lure Montag into reading more books so that humanity would not be so ignorant.