I'm going to use an old reply:

The two chief reasons for the cultural revolution were internal politics and ideology.

After the failure of the great leap forward Mao had being sidelined from power and the day-to-day running of the government was taken over by Liu Shoaqi and Deng Xiaoping. The cultural revolution started off as a play by Mao to attack those two leaders for ideological impurity, for being "capitalist roaders" whose pragmatic style of governance was leading China away from the road towards Communism. To this end he was successful in purging both Liu and Deng from the government and reasserting himself as the unquestionable leader of China.

The second explanation was that the "continuous revolution" was something Mao genuinely believed. He did believe that the Communist party and its cadres had indeed accumulated a large degree of privilege and corruption had became a problem. It was not just him who believed this: both Deng and Liu had started off supporting the cultural revolution when it began and before it became obvious how violent it was to become. He believed that there was a need to train up a new generation of revolutionaries to take the mantle of the old generation and renew China's revolutionary zeal. The best way to train a new generation of revolutionaries was, well, to have them make a revolution, even against the party and the state Mao himself had built. Had the cultural revolution simply being a cynical political stratagem to for Mao to purge his opponents it could have ended in 1966 when Liu and Deng was purged, yet it went on for 10 years longer and inflicted considerable damage to the party and the state.

When it comes to geopolitics one could see the cultural revolution as ideologically defining Chinese Communism apart from Soviet Communism and trying to forestall the development of a Soviet-style bureaucratic state in China. And indeed China was deeply hostile to the Soviet Union during the late Mao period, accumulating in the tactful Sino-American alliance aimed at the USSR. But the primary explanation for it was never geopolitics or foreign relations, it was internal politics and what kind of society Mao wished to build in China.

Source: Mao's Last Revolution by Michael Schoenhals and Roderick MacFarquhar

Turbulent Decade: A History of the Cultural Revolution by Y Jiaqi