Faber is first naturally afraid of Montag when they meet. Montag is a fireman. Instead of our understanding of firemen today, men who help put out fires so that people can be protected from harm, the firemen of Fahrenheit 451 instigate fires on homes that allow learning to occur through books. Therefore, Faber's first response to Montag's appearance is one of suspicion. Faber wondered if Montag was maybe investigating to see what he could get Faber to confess.
As Montag reveals more and more curiosity about books and as he demonstrates a sincere desire to learn, Faber's fear softens. I believe he remains skeptical because his language suggests many benefits of books without opening them and showing Montag evidence of books. Montag is the first to show evidence of a book, and this develops trust between the two which is the opposite of fear. As the two grow united in purpose to destroy the establishment, Faber's fear continues to subside.