In my view, after Montag kills Beatty, realizing that he allowed himself to be killed, Montag comes to a greater appreciation for the fight against censorship. It is obvious that Beatty was miserable as a fireman, with all his knowledge of literature which apparently shows he had a great love of books.
Montag realizes that since Beatty would rather die than live in a world devoid of literature and the pleasure of reading. Montag's purpose and his life have greater meaning.
Montag has burned his old life, severed all ties. He is now free to find a way to change the society he lives in, unlike Beatty who could not be free in the society he lived in, his only escape was death.
Montag realizes that Beatty wanted to die: "In the middle of crying Montag knew it for the truth . . . He had just stood there not really trying to save himself . . ." (108).
There are two ways to look at this.
First, is Montag just telling himself this to ease his guilt? When reading the showdown between Montag, holding the flamethrower and having just burned his house and books, and the defenseless Beatty, it seems that Beatty does not expect Montag to really go through with it. Remember, for much of the novel, Beatty has been able to confuse and manipulate Montag. Why should he think any different now?
However, when one thinks of the themes inherent in the novel, such as apathy and passivity and alienation and loneliness (http://www.enotes.com/fahrenheit-451/themes), it is not that hard to believe that Beatty could simply be tired of living a life devoted to destruction.