The political split between the Soviet Union and China began when the relatively harmonious relations between the two countries became acrimonious in 1959 after Khrushchev opened talks with the USA in pursuit of his policy of “peaceful coexistence”.
Khrushchev-Eisenhower meeting: "American Stooge"
Even worse from Mao's point-of-view was Khrushchev's proclamation of the idea of "peaceful coexistence," that the tenet of inevitable armed conflict between the capitalist and communist "camps," a basic tenet of Marxism-Leninism-Stalinism-Maoism, was not inevitable. Khrushchev felt that nuclear weapons had changed the equation, and that because of those weapons, communism and capitalism would avoid armed conflict. Mao felt that Khrushchev was retreating from an active, violent struggle for the triumph of communism.