As I recall, Keating told the boys when things went too far in the auditorium that "sucking all the marrow out of life doesn't mean choking on the bone". What he was saying to them was yes, seize the day - but don't lose sight of reality or consequences as you do it. There is a balance to be had. Seizing the day at the expense or harm of others is not acceptable. We cannot do whatever we want to do to please ourselves without considering the cost. In the end, Neil wasn't willing/able to pay the cost, i.e. standing up to his father.