Montag begins to see his world as an outsider might. Prior to this, he had seen it as others told him to, for the most part. He draws strength from meeting the young woman, and begins to think for himself; Montag is forced (by his own mind) to deal with the reality of truths and lies. He becomes more conscious of right and wrong, then acts on that knowledge. Because she seems free in a sense he is not, he begins to desire that freedom. Montag also admires her fearlessness and emulates it.
This is a huge turning point for Montag. When the call comes in, the firemen go as usual. However, the woman refuses to leave her home and her books. They burn her as well, and Montag is haunted by the vision. He had suspected up to this point that what they were doing was wrong...the complete annihilation of books and contrary thoughts and anything against the government...but when they burn the books regardless of the loss of human life, he is convinced. This is also the time when we know he intentionally takes a book from the home. He stashes it with all the others, which the reader is almost shocked to read about. Until this point, we do not know Montag has hidden books in his home. Even his wife is clueless on this fact.
Montag becomes ill and does not go in to work the next day. His boss comes to the home and hints that the book needs to be brought back in to be burned...he knows that Montag has taken a book from the burn site and that every fireman suffers from this same illness. They have complete confidence that Montag will recover from his illness and return to work soon to join his fireman brotherhood and continue the stamping out of thinking in their world.