The Sino-Soviet split came about in part because of the two countries’ different interpretations of Marxism and in part simply because each country wanted to have more power.
The communist parties in the Soviet Union and China had some differences of opinion regarding communism. For example, the Soviet communists held that communism could only come about through the efforts of the workers. This brought them into conflict with the Chinese, who thought that communism could be brought about by the peasants. More importantly, perhaps, the Chinese and the Soviets disagreed on how communist countries should interact with the West. Mao Zedong wanted the communists to be very aggressive with the West. By contrast, the Soviets (particularly after Stalin’s death) were more inclined to believe in peaceful coexistence. These ideological differences helped to make the split possible.
However, the split was not all about ideology. It was also about nationalism and power. China did not particularly like being the junior partner of the USSR. It was unhappy because it did not think the Soviet communists had treated it well before and during WWII. The Chinese were angry because the Soviets would not share nuclear technology with them. In addition, China simply wanted more power. It wanted to have more control over communist countries like North Korea. It did not want to just be a satellite state of the USSR.
Thus, we can see that the Sino-Soviet split was caused partly because the two countries’ communist leaders disagreed about communism and partly because the two countries each wanted greater power for themselves.