Firstly it is a must to understand the society into which this book is set. This book is set in 1959, this era, especially in the United States, is one of extreme conservatism. This society was one, where parents made all of the decisions for their children, where the wishes of the child were are ignored and where schools like Welton Academy were expected to produce students that would attend Ivy League colleges, 8 top North Eastern American college. So when Mr. Keating arrived at the school and tells the students to start to take on new challenges to try and get the most out of their lives, to enjoy the beauties of poetry and to not allow the cynicism of the 1950s get to them and make them hoi polloi (Greek term for the herd.) His actions lead the students to start to challenge the society they once readily accepted and therefore all the futures that had been planned years before. They students start regularly breaking the rules and reform a secret society called “The Dead Poets Society”. The resulting clash of the students against the society results in some of the students getting positive results like Todd Anderson finally able to confront his parents and take control but some have negative results like Neil Perry committing suicide as he can not lead the life he wants.
Maybe people from today cannot really understand what is so controversial, because today it is quite normal for young people to completely make their own decisions about what they want to do in the future.