How we cite our quotes: All quotations are from The Breakfast Club.
Quote #1
BRIAN: Saturday, March 24, 1984. Shermer High School, Shermer, Illinois, 60062. Dear Mr. Vernon, we accept the fact that we had to sacrifice a whole Saturday in detention for whatever it was we did wrong. What we did was wrong. But we think you're crazy to make us write an essay telling you who we think we are. What do you care? You see us as you want to see us—in the simplest terms, in the most convenient definitions. You see us as a brain, an athlete, a basket case, a princess and a criminal. Correct? That's the way we saw each other at 7:00 this morning. We were brainwashed.
They were brainwashed because they all made assumptions about each other—letting their respective cliques and stereotypes determine their judgments. The whole plot of the movie involves reversing those judgments.
Quote #2
VERNON: All right people, we're going to try something a little different today. We are going to write an essay—of no less than a thousand words—describing to me who you think you are.
BENDER: Is this a test?
VERNON: And when I say essay, I mean essay. I do not mean a single word repeated a thousand times. Is that clear, Mr. Bender?
BENDER: Crystal.
Vernon is telling them to write an essay about who they think they are—but he already thinks he knows who Bender is: the kind of kid who makes a joke out of everything. Not that Bender doesn't do that, but, in a way, he's just fulfilling the expectations people like Vernon set for him. If they didn't have those expectations, maybe he would behave differently.
Quote #3
BRIAN: Who do I think I am? Who are you? Who are you? I am a walrus.
Brian is musing on the question Vernon's assigned them. It's possible that he's thinking of the first line from John Lennon's "I am the Walrus": "I am he as you are he as you are me and we are all together." That's basically what they all realize at the end of the movie: All the students identify with each other instead of with their personal stereotypes.