Prior to Montag's "awakening" inspired by his talks with Clarisse, Faber, and his own (Montag's) courage and curiosity, Montag was one to burn rather than face his problems. In fact, burning a problem was equal to ignoring it altogether by destroying it. As Montag begins questioning things, he starts to summon the courage to face problems. This involves asking questions (of others and himself) and really trying to understand why books are burnt. One general irony regarding this statement is that Montage realizes that he had been part of the problem. He realizes that firemen (aka censorship), not books, are the problem. The particular irony regarding Beatty's statement is that, as Montag's most immediate authority figure, Beatty is a major part of the problem. The irony is that Montag will eventually face (and burn) the problem: Beatty himself.
Not only does Montag face Beatty (thereby contradicting Beatty's original maxim) but he also burns him. This is ironic because Beatty suffers the same fate as the books. Beatty has been the destroyer and now he is destroyed by his own weapon.
There is also some poetic irony here (and poetic justice). Beatty is a hypocrite. He is well read but he burns books. Even in his waning moments, he quotes from Julius Caesar in order to intimidate Montag, but it only confirms Montag's resolve. Beatty uses literature to support his point, but his point is to eradicate literature. Montag sees through this hypocrisy.