Final answer:
Malcolm X's 1964 extremist quote challenged the nonviolent approaches of the mainstream civil rights movement, reflecting his support for self-determination, Black Nationalism, and the right to self-defense amidst racial oppression.
Step-by-step explanation:
In 1964, Malcolm X's statement, “You show me a black man who isn't an extremist and I'll show you one who needs psychiatric attention,” was directly challenging the mainstream civil rights movement's strategies of nonviolent protest, integration, and assimilation. Malcolm X was advocating for a more militant and confrontational approach to dealing with racial injustice, aligning more with the ideologies of Black Nationalism and self-determination. This philosophy of seeking empowerment outside the established means was rooted in the belief that African Americans could not thrive in an atmosphere of white racism and needed to take complete control of their own communities, cultures, and livelihoods.
Malcolm X, having associated with the Nation of Islam, was critical of the nonviolent strategies of other civil rights activists and maintained that violence in self-defense was appropriate. He famously shifted his focus towards a global understanding of oppression against blacks after his pilgrimage to Mecca and founding the Organization of A-f-ro-American Unity, but he continued to emphasize the need for dramatic and substantive changes in the lives of African Americans. His rhetoric reflected a deep frustration with the slow pace of progress and the persistent inequalities faced by blacks in the United States.