What two reasons did Montag give for burning the books in 1984?
If you are referring to the conversation between Montag and Clarisse at their first meeting, his reasons are simple: It's against the law to have unapproved books and it's fine work that he enjoys. The sense we get of Montag early on is of someone who hasn't thought independently in a long time, perhaps his whole life. The work of a fireman makes sense to him.
He mentions how he likes the smell of kerosene on his clothes, the schedule, the black and white rationale of it all. Clarisse is the problem with this. She interrupts his regimented, flaming, detached life with simple, yet troubling, questions such as "Are you happy?". Montag is forced to reevaluate whether he likes his job, his life, and the answers for him become complicated.