The unusual thing that happened during the fire was that Montag stole a book during the fire.
In Montag’s world, firemen do not put out fires—they set them. Books are illegal, so anyone accused of having them has his or her house burned. Houses are fireproof, books are not. Montag and his firemen crew are called to the house of a woman suspected of having books. Not only does the woman, Mrs. Blake, have these books, but she actually chooses to burn herself alive with the books as opposed to being arrested and watching the books burn.
Montag is so fascinated by the idea of what is in the books, and what would make the woman die for them, that he steals one.
Now, it plunged the book back under his arm, pressed it tight to sweating armpit, rushed out empty, with a magician's flourish! Look here! Innocent! Look! (Part I)
Montag never considered anything other than what society expected of him until he met Clarisse, his neighbor. She was a young lady who asked him if he was happy. She got him questioning himself, and he began to question the world around him. He started to wonder why books were illegal, and what might be in them. Out of curiosity, he took one. It was the beginning of his awakening, and the point where he had to make choices. Up until this point, Montag was like everyone else, he had no choices.
Montag stole the book because he wanted to know what made it worth dying for. He wanted to know why the old woman would take such a risk, and why she would give her life. He also wanted to know why the book would be banned, and why it was so terrible that it needed to burned. Beatty was aware of what was in the book, and aware that Montag was asking questions. He tried to explain to Montag that a society where everyone was happy, and no one asked questions, was a better society. Most people never saw the books. Most people never asked. They lived life feeling what they were told to feel.