To me, the essence of the film is summed up in the note at the end:
Dear Mr. Vernon
We accept the fact that we had to spend a whole Saturday in detention for whatever it was we did wrong, but we think it's stupid for you to make us write an essay telling you who we think we are. You see us as you want to see us. In the simplest terms with the most convienient definitions. But what we found out is that each of us is a brain, an athlete, a basketcase, a princess, and a criminal. Does that answer your question?
Sincerely Yours, The Breakfast Club
Brian Johnson: I'm a f#&king idiot because I can't make a lamp?
John Bender: No. You're a genius because you can't make a lamp.
Richard Vernon: What if your home... what if your family... what if your *dope* was on fire?
John Bender: Impossible, sir. It's in Johnson's underwear.