How we cite our quotes: All quotations are from The Breakfast Club.
Quote #1
And these children
that you spit on
as they try to change their worlds
are immune to your consultations.
They're quite aware
of what they're going through. —David Bowie
These lyrics from the Bowie song "Changes" appear on a black screen at the very beginning of the movie. It helps state part of the message of the movie—the idea that adults don't remember what it's like to be young, and that teenagers are capable of working out their own lives. They're "immune to your consultations" because they understand their lives better than the people giving the consultations do.
Quote #2
BENDER: Were you or were you not motioning to Claire?
BRIAN: Yeah, but it was only... was only because I didn't want her to know that I was a virgin, okay? Excuse me for being a virgin, I'm sorry...
CLAIRE: Why didn't you want me to know you were a virgin?
BRIAN: Because it's personal business, it's my personal, private business.
Brian is a virgin—unlike Bender (presumably). It's another thing that divides them, and heightens their respective identities as Brain and Criminal. Unbeknownst to Brian, Claire's actually a virgin too (as, apparently, is Allison)—but she neglects to mention that detail here, probably for the same reason Brian doesn't want to admit it. But when the truth comes out, it's another point demonstrating that they're closer together than they all realized.
Quote #3
ANDREW: Um, I'm here today... because uh, because my coach and my father don't want me to blow my ride. See I get treated differently because uh, Coach thinks I'm a winner. So does my old man. I'm not a winner because I wanna be one... I'm a winner because I got strength and speed. Kinda like a racehorse. That's about how involved I am in what's happening to me.
Andrew is growing up and feels like he should have some control over his own life, naturally. But that's the exact opposite of what's happening to him—he feels "like a racehorse" because he feels like the property of the adults around him. Allison doesn't think this is an honest answer to the question she asked him (Why are you in detention?), which is true—but it is an honest revelation of a particular truth about him.
Quote #4
EVERYONE: C'mon, answer the question. Come on. Answer it.
BENDER: C'mon, it's easy. It's only one question.
CLAIRE: No, I Never did it!
ALLISON: I never did it either. I'm not a nymphomaniac, I'm a compulsive liar.
This is the moment when Claire—like Brian, earlier—admits that she's never had sex. Then, Allison admits it too, despite having just said the reverse. Allison's Weird Girl powers grant her the magical ability to ferret truths out of people. Here, she helps break down the distance between herself, Claire, and Brian; they share something in common. It helps shatter Claire's mystique, too.
Quote #5
ALLISON: When you grow up, your heart dies.
BENDER: Who cares?
ALLISON: I care...
Why does Allison think that adults have dead hearts? Presumably, it's because they don't feel passionately about things once they're older. They've been numbed by their everyday lives. This is appealing to the teenagers in the movie, but numerous real-life adults would probably object to the notion that their hearts are dead.
Quote #6
BRIAN: [...] But what we found out is that each one of us is a brain...
ANDREW (VO): ...and an athlete...
ALLISON (VO): ...and a basket case...
CLAIRE (VO): ...a princess...
BENDER (VO): ...and a criminal...
BRIAN (VO): Does that answer your question? Sincerely yours, the Breakfast Club.
This is the big revelation they all receive at the end of the movie. The five students discover common ground between each other, and realize their experiences aren't actually so far apart. There are lots of points of contact between them: They experience pressures to conform, have issues with their parents, etc. It allows four of them to connect romantically, and allows Brian to—you know—write everyone else's essay for them.