African-Americans simply weren't getting their constitutional rights enforced. Which is exactly what Dr. Martin King and Minister Malcolm X were trying to accomplish. They wanted African-Americans to have the same freedom as any other American in the country, they just had two different approaches. The MLK approach was to show the country that they were freedom fighters fighting for freedom, but they weren't trying to destroy the country. Just the system that held them down and were going to accomplish it by exercising their constitutional rights of Freedom of Speech and Assembly.
Malcolm X's approach was different, that the way to destroy the system, was by any means necessary, even if that means violence. That what they were fighting for which was their own freedom just as the Caucasian community had, should already be theres. And that the racists should just get-out-of-the-way, or they'll be run over. That there wasn't any negotiation, because African-Americans already had the freedom under law and under the Constitution that every other community had in America. Which meant that racist Southern Anglo-Saxon bigots and other racist Caucasians, should either step aside, or they'll be forcefully removed by the African-American community.