The night before, Montag saw a woman die with her books. She burned with them. This started Montag thinking that you just don't kill yourself and burn yourself for nothing. He wants to discuss this with Mildred, but Mildred is a government person. She has become the pleasure-seeking person that the government has fostered. Montag's arguments are:
"There must be something in books, things we can't imagine, to make a woman stay in a burning house; there must be something there." (pg. 51 - Part I)
He also says:
" ... for the first time I realized that a man was behind each one of the books. A man had to think them up. A man had to take a long time to put them down on paper. And I'd never even thought that thought before." (pg. 51-52 - Part I)
"It took some man a lifetime maybe to put some of his thoughts down, looking around at the world and life, and then I come along in two minutes and boom! it's all over." (pg. 52 - Part I)
So his two arguments are (1) that if it took a lifetime for some man to write a book, the least they could do is read it, and (2) that there must be something important about books if someone is ready to die for them.
However, it falls on deaf ears. Mildred says:
"You want to give up everything? After all these years of working because one night some woman and her books...." (pg 51 - Part One)