On what basis did the supreme court rule the constitution protected student right to wear black armbands as a sign of protest?

The First Amendment to the Constitution guarantees that the students have the right to express their political views as long as it don’t disrupt school or invade the rights of other students. And since wearing a black armband in school as a sign of protest was not disruptive, the Supreme Court have found that freedom of speech and show of opinion in public schools must be protected. This rule is in favor of Mary Beth Tinker, a 13-year-old girl who wore black armbands to school as a protest to the Vietnam War.