Pay particular attention to a very important character: Captain Beatty. What role in Montag‘s life does he seem to inhabit?

Beatty plays the role of authority or father figure to Montag throughout much of the novel. He is the boss at the firehouse. When we first encounter him in the text, he plays the role of disciplinarian, the father from whom Montag has to hide his thoughts. For example, when Montag expresses his fear that the Mechanical Hound will turn on him, Beatty becomes accusatory:

"Why? You got a guilty conscience about something?"

Also like a father figure, Beatty upholds the existing order as all powerful, saying:

"Any man's insane who thinks he can fool the Government and us."

It is Beatty, the symbol of authority, who lays down the law with the woman who doesn't want to leave her house full of books. Montag expects him to fill this role. Beatty speaks to the woman as one might a child:

"I'm counting to ten," said Beatty. "One. Two."

Beatty, like a father, has already seen everything Montag is going through in being attracted to books and has his pat answers ready. Beatty says:

"I've seen it all. .... Every fireman, sooner or later, hits this. They only need understanding, to know how the wheels run. Need to know the history of our profession. They don't feed it to rookies like they used to.

Beatty has read many books, though he completely sides with destroying them. He has many literary references at his fingertips, showing his superior knowledge, just as a parent might.
Finally, Montag has to kill Beatty to get free of his grip. Most children don't literally kill their parents, but most have to struggle for independence from them in order to forge their own paths.