How we cite our quotes: All quotations are from The Godfather.
Quote #1
MICHAEL: My father made him an offer he couldn't refuse.
KAY: What was that?
MICHAEL: Luca Brasi held a gun to his head, and my father assured him that either his brains or his signature would be on the contract.
KAY: ...
MICHAEL: That's a true story.
(cut to Johnny singing, then back to Michael)
MICHAEL: That's my family, Kay. That's not me.
Michael tries to assure Kay that he's not into the kind of violent activity that characterizes his mobster family… but, as it turns out, he actually is. In fact, his calmness and coolness make him even more effectively ruthless.
Quote #2
LUCA BRASI: Don Corleone, I am honored and grateful that you have invited me to your home on the wedding day of your daughter. And may their first child be a masculine child.
Brasi is expressing an Old World preference for sons over daughters. It's quite sexist, obviously. This is a definite part of The Godfather's world: the men of the family exclusively call the shots.
Quote #3
TOM HAGEN: Mr. Corleone is Johnny Fontane's godfather. Now Italians regard that as a very close, a very sacred religious relationship.
This illustrates the importance of family to the Corleones—but their family ties are cemented through loyalty and by repaying favors. Johnny Fontane and Don Corleone use their relationship as an occasion to help each other out in a way that is both familial and businesslike.