What false promises is Beatty referring to?
In Part Two of Fahrenheit 451, Montag shows Mildred his stolen copy of the Bible and she tells him that he must hand it over to his boss, Captain Beatty. Montag doesn't want to, prompting Mildred to shriek that he must make a choice between her and the Bible. It is in this melee that Montag hears the voice of Captain Beatty, encouraging him to relinquish his collection of books:
"All the silly things the words mean, all the false promises, all the secondhand notions and time-worn philosophies."
In other words, Beatty wants Montag to stop believing in the power of books and to accept that books will not make him happy or satisfied with his life. To convince Montag of this, Beatty tells him that books contain "silly things" and "false promises." In Montag's thoughts, Beatty says this while "perspiring gently" which suggests that Beatty is nervous because he is lying. In truth, Beatty knows that books contain the answers which Montag seeks and that there is little he can do to stop him from reading.