Although Montag has been moving towards change for a long time, almost unconsciously stealing books and hiding them in his house, it is his meeting with Clarisse and his wife Mildred's near-death that spurs him to start truly questioning the society in which he lives:
"Are you happy?" she said.
"Am I what?" he cried.
Of course I'm happy. What does she think? I'm not? he asked the quiet rooms. He stood looking up at the ventilator grille in the hall and suddenly remembered that something lay hidden behind the grille, something that seemed to peer down at him now.
(Bradbury, Fahrenheit 451, Google Books)
Clarisse offers him a perspective on life that he has never really considered, that the social programming of people to watch TV and repeat its meaningless catchphrases causes those people to grow apart from each other. People no longer have direct friends; they have TV-watching friends, who only visit in order to share a show. Montag has "friends" in the firehouse, but he doesn't really share anything with them. Mildred's near-death, which may have been deliberate, shows Montag that he cannot continue in the same manner as before; something must change, and he looks to Clarisse's example for guidance.