Lyndon B. Johnson assumed the Presidency after the assassination of John F. Kennedy. He was reelected in 1964.
Johnson’s expansion (and Nixon’s continuation) of the Vietnam War angered many, and Bill Ayers and others in Students for a Democratic Society formed a revolutionary cadre to attack symbols of American imperialist power. They aligned with the Black Panthers and other revolutionary groups to form a network of anti-imperialist, anti-racist and anti-capitalist opposition.
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The song title, of course, is a critique or commentary on America and its relationship with Black folks. The substitution of a “k” for the “c” (often spelled “Amerikkka”) is a long tradition among black Americans critical of the nation.