In the case of Tinker, it was "a silent, passive expression of opinion, unaccompanied by any disorder or disturbance. Where in Fraser when he slipped a sexual metaphor into a speech and was suspended for it, the school was in it's authority to do so
school boards know that peer pressure is perhaps "the single most important factor leading schoolchildren to take drugs". Congress has also declared that it is part of a school's job is educating students about the dangers of illegal drug use.
Because the banner had a reference to illegal drugs. The Principle had to act, failing to do so would send a powerful message to the school body on how serious the school really is on illegal drug use.
Under the context of the 4th amendment and other previous cases. While children do not shed their constitutional rights at the schoolhouse gate, the nature of those rights is what is appropriate for children in schools.