In my opinion, Guy Montag wants to change the society he lives in because he does not feel like he is living a truly human life. I think that he truly comes to realize this when he meets Clarisse and when he sees the old lady die with her books.
I think that Montag wants to have real feelings -- he wants to care about other people. I think he also wants to have thoughts. Both of these are things that are more or less contrary to the values of his society.
Montag is living in a marriage that is not based on love. He and Millie can't even remember where they met and she, at least, shows no signs of caring about him. I think that he wants that to be different.
Montag is living in a society where he is not encouraged to think deep thoughts. I think he wants that to change as well -- he wants to be able to think about things without all the distractions his society throws at him (symbolized by the Denham's Dentrifice ad).
To be human, you have to be able to feel things like love and you have to be able to think deep thoughts. Montag lives in a society where these things are not encouraged and he is sick of it -- he wants to be fully human.