To question authority is to challenge it. It's dangerous to those who are seeking to maintain that authority, whether it's in Bradbury's fictional sense or whether it's in a real dictatorship in the present day. Take North Korea, for example, where independent art, thought, press or speech are strictly forbidden. Kim Jong-il and his father before him have maintained power through conformity for more than 65 years in that nation.
In this story, the idea of independent thought and action has been so thoroughly removed from society that Montag is shocked and surprised to hear it so easily and readily from this teenage neighbor, Clarisse, who shatters his world of conformity by almost forcing him to think on such simple and fundamental issues as his personal happiness.