The first clash between Beijing and Moscow is considered to be a discussion about the results of the XX Congress of the CPSU and Nikita Khrushchev's report on the cult of Stalin's personality. Despite the fact that the subsequent VIII Congress of the CPC, which raised the topic of China's industrialization, proclaimed reliance on the Soviet experience of socialist construction, these actions of the CPSU leadership became a reason for the CPC, but not a motive for further ideological and political demarcation.
The development of a new party line began in China after the VIII Congress, and the most important reason for it was the report of N.S. Khrushchev. The speech of the Soviet leader against Stalin and his nomination of a number of accusations of carrying out repressions and other acts incompatible with socialist legality were used by the leaders of the Chinese Communist Party to critically approach this experience of the Soviet Union.
In addition, to the indignation of the Chinese and other delegations was the fact that this report itself was read out without their presence behind closed doors, since they were simply not allowed into the meeting room. The text of the report itself was never transmitted to the CPC Central Committee, which led to the fact that Beijing had to formulate its position based on those notes made by Chinese communists from a copy of the draft version of N.S. Khrushchev's speech, as well as from the translation of the publication of the American edition of the New York Times about the last XX Congress of the CPSU. 
In fact, using these events in Beijing, they began to form a new party course, since, according to Mao, criticism of the cult of personality shook the basic foundations of the theory of building socialism and they had to solve the theoretical and practical problems that arose independently.
At the same time, it should be noted that the differences expressed by the CPC were used as a pretext for the decisions of the XX Congress of the CPSU, but there were other issues behind this pretext. It is characteristic that for several years after the XX Congress (February 1956), its decisions were fully recognized publicly by the Communist Party of China. Thus, the CPC brochure for April 1956 says: "The XX-th Congress of the CPSU [...] made a number of important decisions. These decisions concern the consistent implementation of Lenin's course on the possibility of peaceful coexistence of countries with different social systems, the development of the Soviet democratic system, consistent observance of the principle of collegiality within the party, criticism of the shortcomings of the party [...] The Congress mercilessly exposed the cult of personality that has long spread in Soviet life, which entailed many mistakes in work and had unpleasant consequences."
In addition, the decisions of the XX Congress were adopted as a guideline for all socialist countries and at a meeting of 12 socialist countries in Moscow in November 1957, where the delegation of the Communist Party of China was headed by Mao himself. The Declaration emphasizes that "the historical significance of the XX Congress of the CPSU for the further development of the international communist movement on the basis of Marxism-Leninism". At the same time, the same Declaration notes that "The Communist and Workers' Parties participating in this Meeting declare that the Leninist principle of peaceful coexistence of the two systems, which has been further developed in modern conditions and decisions of the CPSU Congress, is the unshakable foundation of the foreign policy of socialist countries and a reliable foundation of peace and friendship between peoples." 
The same assessment was confirmed in the Declaration of the 81st Communist Party in Moscow in November 1960.
As we will see further, the main deterioration in relations between the two countries occurred after the XXII-th Congress of the CPSU in October 1961. Relations between the USSR and the PRC worsened when the Chinese leadership was not satisfied with the position of the USSR in 1962 on the border dispute with the PRC (October-November 1962), since the USSR considered the invasion of the PRC into India unfair, regarding it as a violation of the agreement between the PRC and India (1954) regulating border disputes between the two countries.
However, going back to the beginning of this process Mao Zedong gave his assessment of the new Soviet leadership at the plenum of the CPC Central Committee on October 9, 1957 as follows: "First of all, we have contradictions with Khrushchev on the issue of Stalin. We do not agree that he is trampling Stalin into the mud. After all, he blames Stalin to the point of outrage. And this already concerns not only one of their countries, but all countries. Our installation of a portrait of Stalin in Tiananmen Square meets the aspirations of the working people of the whole world and shows our main differences with Khrushchev."
This position fully emphasized both the tribute to tradition and continuity in the communist movement, and also demonstrated the independence and independence of Chinese politics, and the fear that total criticism of Stalin's personality could spread to Mao Zedong himself. The fact is that by that time the cult of the personality of its chairman, as the helmsman of the Chinese people, began to develop in the PRC, and this turn of the leadership of the CPSU hit him personally.
Formally correctly criticizing the leaders of the CPSU for the "course of the XX Congress", which was indeed a turning point in the construction of socialism in the USSR, the Chinese leadership made completely incorrect political conclusions. Mao Zedong seriously argued that de-Stalinization was a form of rebirth of the Soviet Union and its rejection of the socialist path of development. Moreover, it was allegedly damage to the process of restoration of the capitalist system. Later, already in the 60s, this attitude would lead to the development by Mao Zedong of a special theory of "social imperialism" in relation to the USSR.
Therefore, these conclusions really became a turning point, as the leadership of the CPC comes to the conclusion that it is necessary to develop an independent line, which was later expressed in a fierce struggle for leadership in the world communist movement and the socialist camp. At the same time, such a position was justified by the need to fight Moscow's revisionism and preserve the principles of Marxism-Leninism, which were now defended exclusively by the Chinese Communist Party, as they themselves were claiming.
However, the defense of these principles was clearly using «ultra-left» radical slogans. In particular, the object of attack by the leadership of the CPC was the thesis of the Soviet Communist Party on the peaceful transition from capitalism to socialism, voiced by Nikita Khrushchev at the same XX Congress of the CPSU. Yes, indeed, this point clearly contradicted the Marxist-Leninist theory, but it can be interpreted as the desire of the leadership of the USSR at that time to avoid a third world war through the so-called peaceful coexistence of the two systems in order to ensure the possibility of calm economic development and socialist construction in those countries where the Communist parties were already in power.
This position was rejected by the leading figures of the Chinese Communist Party, who considered it unrealistic and impossible in principle. In the situation of attempts by imperialism to stop the collapse of the colonial system and unleashed wars and interventions in Indochina, such a view seemed to be a real irony. But if the criticism of such a position of the CPSU was largely justified and correct, then Beijing's attacks on Moscow's thesis about the necessity and possibility of preventing a global war led to the promotion of petty-bourgeois adventurist ideas and slogans that have nothing in common with the class approach and Marxist analysis.
We are talking about the idea of a nuclear world revolutionary war. Thus, at a joint meeting of communist and workers' parties in Moscow in November 1957, the chairman of the Chinese Communist Party announced the concept that even if half of humanity is destroyed in the event of a nuclear conflict, the second, represented by the victorious peoples, "will create a thousand times higher civilization on the ruins of imperialism than under the capitalist system, will build their truly wonderful future."
As we can see, this "revolutionary war" seemed to be a positive phenomenon, despite the death of most of the working class and working people, since in this way it would completely destroy the capitalist basis and this world system itself. At the same time, Mao Zedong and the majority of the CPC leadership were confident that in the end it would be the unconditional victory of the socialist system, despite the fact that the productive forces and large masses of the population in the core of the socialist camp, namely in the USSR, would be destroyed.
Mao even concretized his thoughts within the framework of his report, trying to justify his unsupported optimism about the possible number of dead: "Is it possible to assume how many human casualties a future war may cause? Perhaps it will be one third of the 2,700 million population of the whole world, i.e. only 900 million people. I think it's still not enough if atomic bombs are really dropped. Of course, it's very scary. But it wouldn't be half as bad... If half of humanity is destroyed, then there is still half, but imperialism will be completely destroyed and there will be only socialism in the whole world."
Beijing also proceeded from the idea that large masses of the Chinese population provide undeniable advantages for the PRC, since in the event of a thermonuclear third World War, the losses for the people would not be so critical. Mao Zedong did not rule out the death of 300 million Chinese, but mathematically deduced that the remaining 300 would be able to fully master the deserted lands and establish a new world center of socialism. At the same time, the leadership of the CPC believed in the inevitability of such a global clash in the near future.
This attitude and Beijing's practical policy in the Asia-Pacific region was already clearly in conflict with the foreign policy of the USSR, which then sought to avoid being drawn into local regional conflicts in order to prevent open armed confrontation with the United States. The fact is that in addition to the world revolutionary nuclear war, in 1958-1959 the leadership of the CPC put forward a new line in its foreign policy activities, named in the national style as follows: "sit on a mountain and watch the struggle of two tigers." 
This concept was to provoke a conflict between the Soviet Union and the United States and thereby achieve the realization of their strategic interests in the region. In essence, this meant the desire of the Chinese Communist Party to force the Kremlin to follow the path of Mao's theoretical developments about the inevitability of the intensification of the armed struggle of the socialist camp with world imperialism.
It was during this period from 1957-58 that the situation in the waters around the island of Taiwan sharply worsened, where the last Kuomintang forces settled, which received direct military and political assistance from Washington. Then, as now, Beijing demanded the annexation of Taiwan to mainland China and assumed that the USSR would act as one of the participants in the clashes. In response to the shelling of the islands of Kinmen and Matsu in the Taiwan Strait by the People's Liberation Army of China (PLA), the US administration has advanced the forces of its Pacific fleet equipped with nuclear weapons.
At that moment, Moscow took a position of non-interference in the conflict, based on the fact that its escalation was not coordinated with it by the Chinese leadership, thereby actually distancing itself from Beijing's actions. It was only after the new Taiwan conflict began to subside in October 1958 that Nikita Khrushchev sent Eisenhower a formal letter of protest.
Such a denouement of the situation has become another and more serious factor of the separation between the CPSU and the CPC and a turning point in relations between the socialist countries. Beijing's response was the refusal in October of the same 1958 to Moscow's proposal to place a submarine base and a tracking radar station. That is, measures of real protection were rejected on the move in the event of a new aggression by the US Navy.
This fierce controversy between the USSR and the People's Republic of China was also heated up a lot by the domestic political course. The fact is that 1958 Mao Zedong proclaimed a "new general line" in building socialism. The experiment of the "three red banners" (the "general line", the "big race" in industry, as well as the creation of "people's communes" in villages), had terrifying socio-economic consequences. This «ultra-left» course had nothing to do with the Soviet experience and ignored the progressive development of industrialization and collectivization in the 30s, divided into several five-year plans.
As a result of the voluntarist policy, a number of regions of China were seized by famine, and entire sectors of the national economy were paralyzed. The Soviet leadership, not without reason, considered the Chinese attempts to build their own socialist society in three years, without regard to the real backward base and without Moscow's scientific and technical support, erroneous, adventurous and dangerous for the interests of the USSR.
At the same time, in China itself, in 1957, the first anti-Soviet campaign began for the first time. It was unleashed within the framework of the internal political course "let a hundred flowers bloom, let a hundred schools compete", when the CPC Central Committee allowed part of the intelligentsia and various near-party and non-party groups to discuss the further development of socialist construction in order to prevent dogmatism and excesses.
As a result, of course, this discussion at the top of Chinese society, which came out of the pre-revolutionary past, led to negative consequences and anti-communist statements. The desire of this creative "elite" to return the capitalist system became clear to everyone. But while the controversy was going on, anti-Soviet sentiments spread by right-wing elements, which were actively broadcast by the party press, sharply strengthened.
All this together created the basis and prerequisites for a sharp cooling of relations and the start of the process of rupture between the largest socialist countries of the world already in the second half of the 50s. Subsequently, the situation only worsened.
Rightly criticizing the opportunistic tendencies and theses of the leadership of the CPSU about the peaceful coexistence of socialism and capitalism and the possibility of the peaceful coming of communists to power, the leadership of the CPC actually went to the other extreme and justified its own course, expressed in the departure from the USSR, which by the end of the 60s led to a fierce conflict, as well as to the formation of the great Han chauvinism and nationalism.