What case does Montag make to Mildred in defense of reading in Fahrenheit 451?
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.
Montag shows Millie the books he has stashed away in an attempt to communicate to her that reading may be the way out of the unsatisfying lives that have trapped them both. He tries hard to communicate with her, to break through her shell. He tells her, "I'm not happy." He also turns off her view screens and wonders if, rather than driving around at high speeds and running over small animals when she is upset and angry, reading might provide a better answer. He wants her to stop relying on the viewscreens to fill her life. He wants her to give books a chance for 24 or 48 hours because the life they are leading isn't, if they are honest with themselves, working for them. She has attempted suicide and he is at the breaking point with his job as a book burner.
Montag insists on reading to Millie from the forbidden books he has collected, suggesting to her they may contain wisdom that will help them turn their lives around. He also talks about the wars the government has gotten into and the rumors that while they live well, many around the world are hungry and toiling:
We've started and won two atomic wars since 1960. Is it because we're having so much fun at home we've forgotten the world? Is it because we're so rich and the rest of the world's so poor and we just don't care if they are? I've heard rumours; the world is starving, but we're well-fed. Is it true, the world works hard and we play?
He then says to Millie, "maybe the books can get us half out of the cave." Montag appeals to both Millie's self interest and her possible interest in a wider humanity in a passionate attempt to touch her core being and engage her as a partner in a new, subversive path in which books will play a central role. Perhaps through books, they can help mold a better world that won't repeat the mistakes of the past. But she is far too brainwashed to respond with anything but fear and rejection.
Basically, what Guy Montag says to his wife, Millie, is that reading books might improve their lives -- both their own personal lives and the life of the country as a whole.
First (this is at the beginning of Part II), Montag points out that Millie had just had the overdose of pills. He implies that it is because she does not read.
Second, he talks about wars that the country has had. He says that maybe if people read books, they would quit making the same mistakes over and over.