What are common rationalizations with examples of quotes that were used in the book Fahrenheit 451?

To rationalize means to use seemingly logical but often faulty reasoning to excuse or explain away one's behavior.
Mildred seems to represent most of the people in the world of Fahrenheit 451 in rationalizing that she is happy with her life when she clearly is not. We readers know she is unhappy because she has tried to commit suicide. Mildred rationalizes or explains this away by saying she has no memory of the suicide attempt. Then she tries to pretend she is happy watching and participating in the shows on the wall-TVs, even though it is clear this life is leaving her unfulfilled. She says to Montag

It's really fun. It'll be even more fun when we can afford to have the fourth wall installed.

Even though she is not really having fun, she tries hard to believe that she is, repeating the word fun several times and rationalizing that another wall screen will make her life better.
Likewise, Beatty mouths the rationalizations of his society for the way people who protest book burnings are treated and for burning and banning books. For example, Montag asks him what happened to the man whose library they'd burned the week before. Beatty says the man was dragged off to the "asylum." When Montag protests that the man wasn't insane, Beatty repeats the common rationalization for treating a sane person as crazy. Beatty says,

Any man's insane who thinks he can fool the Government and us.

Later when he tries to deal with a woman who would rather die than leave her books, Beatty uses rationalizations for not reading, saying to her that reading books is confusing and makes no sense:

Where's your common sense? None of those books agree with each other. You've been locked up here for years with a regular damned Tower of Babel. Snap out of it! The people in those books never lived. Come on now!

Beatty also explains the common rationalization for banning books to Montag, explaining that smart people used to read books and therefore invite "tortures" from the other kids. It was better for everyone to be equal. Since books could get people thinking and thus start trouble, it was better if nobody had the chance read them. That way, everybody would end up the same and happy:

Surely you remember the boy in your own school class who was exceptionally 'bright,' did most of the reciting and answering while the others sat like so many leaden idols, hating him. And wasn't it this bright boy you selected for beatings and tortures after hours? Of course it was. We must all be alike. Not everyone born free and equal, as the Constitution says, but everyone made equal. Each man the image of every other; then all are happy, for there are no mountains to make them cower, to judge themselves against. So! A book is a loaded gun in the house next door. Burn it.