Morse stated that the sign was promoting illegal drug use and therefore as an educator it was her job to put a stop to it.
Frederick filed suit, alleging that the school board and Morse were attacking his first amendment rights of freedom of speech.
The court with a vote of 5-4, ruled that the first amendment does not prevent educators from suppressing school speech, at school sponsored events and the banner was viewed as promoting illegal drug use. Therefore the school board and Morse won the case.
This case created a standard that students, once on school property, don't have the same rights as other citizens. The freedom of speech of one person isn't nearly as important as the safety and well being of the rest of the student body.
The cartoon is explaining how it's okay for big companies to donate to campaigns due to free speech, but a student can't joke about bongs because it doesn't count as freedom of speech because he's in school.