What quotation in "Fahrenheit 451" relates to Montag's questioning his morals and how?
The most interesting quote in Fahrenheit 451 is when Montag rants against Mildred and her friends, namely Mrs. Bowles:
Go home and think of your first husband divorced and your second husband killed in a jet and your third husband blowing his brains out, go home and think of the dozen abortions you’ve had, go home and think of that and your damn Caesarian sections, too, and your children who hate your guts! Go home and think how it all happened and what did you ever do to stop it?
First, it shows a flawed morality: male sexism against women. Montag (and Bradbury) blame women for divorce, abortion, C-sections, and bad parenting. It's a cheap shot and bad logic. Granted, Montag is an illiterate fireman (caveman), but it shows the sexist gender stereotyping typical of the 1950s working male.
First, women alone can't be blamed for any of these problems. It takes two to get a divorce (husband and wife), be a parent (mother and father), and deliver or abort a baby (mother and doctor). Bradbury should have known better to use his hero to rant against women.
It seems that the knowledge in books is hurting Montag rather than helping him. If books turn unthinking men into sexist men, then Montag is certainly reading the wrong books.
Late into the first part of the book, Montag witnesses a life-altering event when the old woman refuses to walk away from her books when her house and her books are about to be burned. She would rather be burned to death with her books than to live without them. Montag is very shaken by this woman's actions and at home tells Mildred about it. He says to her, in one of the book's most definitive passages, "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. You don't stay for nothing." Montag realizes that the "something" in the books is what the society and the government behind the society does not want people to to have. He realizes that his concept of morality has been wrong and that books can teach him and open up his mind.