At the end of Part 1, Montag breaks the news to his wife that he has about twenty books stored in the air-conditioning duct above the front door. She freaks out and he has to slap her in order to calm her down. The first thing he asks his wife is to support him at the moment because he's never asked her for anything before. Then he says that each of them is in a mess because of the way they solve their own problems: "you and the medicine nights, and the car, and me and my work" (66). The way Mildred solves her problems is to take sleeping pills or to go drive her car at dangerous speeds to relieve stress. His mess is his work. Because of these things, he says that they are both headed for a cliff; in other words, they are both headed for self-destruction.
Next, he says that researching books for what they might be missing in life won't be easy, but if they help one another, they might discover what life's purpose is. Then he appeals to her love for him to help him do this within the next 24 or 48 hours. He then promises that at that point it will all be over and maybe they will discover something to pass on to other people.
Finally, he brings up the woman who burned herself for her books and Clarisse as examples of people who are reasons to take the time to discover what they knew and what she and he don't know. Montag explains as follows:
"The woman, the other night, Millie, you weren't there. You didn't see her face. And Clarisse. You never talked to her. I talked to her. And men like Beatty are afraid of her. I can't understand it. Why should they be so afraid of someone like her? But . . . I suddenly realized . . . I didn't like myself at all any more. And I thought maybe it would be best if the firemen themselves are burnt" (67).
Montag sees that there is something terribly wrong with their society when two women wind up burning or disappearing for believing in books or something different than what the government does. All of these reasons are enough for Mildred to give reading a chance, but she's not as committed to it as Montag is.