There's the ideological reasons that all historically conscious leftists know about and while they were the pretexts for the split, I've come to the position over time that they don't represent the core issue that initiated it. As such, there's a fundamental relationship dynamic that should be clarified before anyone gets into studying the deeper weeds of the various grievances that propelled the split. This dynamic is also the principal lesson of value to AES and socialism today which to learn from in preventing such a catastrophic inter-fraternal relationship rupture from repeating itself under the same lines.

As a background, I would argue that the fundamental problem with the entire Comintern movement post-WWII was that it took the system of democratic centralism from the state level to the inter-state level. This was driven by the noble goal of finally breaking down the petty national divisions that bound human society for all of its existence through grasping the historic opportunity presented by the 20th century socialist revolutions and the historic atmosphere of internationalism.

The problem is that, in practice, inter-state democratic centralism led essentially de facto to the leadership of the socialist bloc by the first worker's state, the USSR. This would not be so intolerable if it weren't for the coincidence that nearly all socialist states that came into existence after WWII, with the sole exception of the DDR, were countries that had been the historic victims of colonialism and imperialist control where the indigenous populations had always yearned to finally take control of their own nations. This was true across the socialist world - of Poland, of Czechoslovakia, of Yugoslavia, of China and of the DPRK. The socialist revolutions were therefore also simultaneously struggles for national liberation. For these countries to win their independence and sovereignty - only to immediately be expected to subsume themselves under Comintern democratic centralism as led by the USSR - posed a serious tension that eventually snapped to catastrophic consequences. Comintern internationalism and inter-state democratic centralism were therefore arguably noble ideas, yet also ultimately idealistic, utopian and unfortunately ahead of their time. Implemented in the context of the mid-20th century, they could only end up clashing with the historical conditions of the USSR's new fraternal socialist partners.

No Soviet leader seems to have truly ever grasped this contradiction, including Stalin. The split with Yugoslavia, through his quite heavy-handed attempt to depose Tito within the CPY and then expelling Yugoslavia from the Comintern, was one of Stalin's actual and serious errors. Kate Hudson's work "Breaking the South Slav Dream: The Rise and Fall of Yugoslavia" argues that this was all precipitated by Tito's refusal to submit to Soviet supervision of its foreign policy under Comintern democratic centralism. MLs of the day largely sided with the USSR and denounced "Titoism" for its introduction of market forces as a horrifying betrayal. Tito's refusal to submit to democratic centralism (i.e. the CPSU) was then portrayed as akin to Trotsky's own actions. Obvious, given the conditions of AES today, principled MLs are more sympathetic to the aims of the CPY, but the Yugoslavs at the time were virtually ostracized. Yugoslavia was then isolated from the entire socialist bloc with all Soviet aid withdrawn and it is alleged by Hudson that the CPSU promoted several purges in the other Parties in Europe to remove "Titoist sympathizers."

This inevitably forced the SFRY to turn to the West and exacerbated its experiment with market socialism, which the USSR denounced, into an outright submission to Western capital in many aspects in order to receive desperately needed assistance for its post-war reconstruction, introducing various institutional contradictions that would later culminate in the IMF debt spiral that the SFRY found itself in the 1980s. The refusal by the CPSU to allow Yugoslavia to propose a Balkan federation with Bulgaria was also perceived by the CPY as Moscow's fear of an enlarged socialist state becoming a rival within the Comintern. The situation deteriorated to the extent that the West's scaremongering tactic of the week became that of the "imminent Soviet invasion of Yugoslavia."

The fracture between the CPSU and the CPY echo the later Sino-Soviet quite tellingly and this is likely by its nature indicative of a general defect in Soviet inter-socialist state policy. In 1989, Deng gave an extremely frank speech to Gorbachev during the latter's state visit on the history of Sino-Soviet relations from the Chinese perspective and he himself characterized it like this:

I should say that starting from the mid-1960s, our relations deteriorated to the point where they were practically broken off. I don’t mean it was because of the ideological disputes; we no longer think that everything we said at that time was right. The basic problem was that the Chinese were not treated as equals and felt humiliated. However, we have never forgotten that in the period of our First Five-Year Plan the Soviet Union helped us lay an industrial foundation.

If I have talked about these questions at length, it is in order to put the past behind us. We want the Soviet comrades to understand our view of the past and to know what was on our minds then. Now that we have reviewed the history, we should forget about it. That is one thing that has already been achieved by our meeting. Now that I have said what I had to say, that’s the end of it. The past is past.

More contacts are being made between our two countries. After bilateral relations are normalized, our exchanges will increase in depth and scope. I have an important suggestion to make in this regard: we should do more practical things and indulge in less empty talk.

https://www.marxists.org/reference/archive/deng-xiaoping/1989/196.htm

The Soviet policy of Comintern and socialist bloc leadership through a form of inter-state democratic centralism by design prevented the treatment of fraternal states as equals. There was already the power, resource and economic asymmetries between the USSR and every other socialist state that prevented any claim to equality on material grounds and all of that combined with such a policy meant counterparts like Yugoslavia and later China found it difficult to see the relationship as one between equals. Given that the USSR's socialist partner states were nearly all countries with histories of national subjugation and thus had a particular desire to be treated as a sovereign and independent polity for once, the potential for relationship conflicts was, in a sense, inevitable and such a dynamic of "inequality" was what Deng himself identified as the actual root problem that defined the Sino-Soviet relationship.

To that end, it could be argued that the USSR carried through with such a mentality all the way to the very end with Gorbachev, who completely went over Honecker's head to discuss the terms of selling out the DDR to Kohl and the US directly, something that Honecker's memoirs written in jail (after being sold out by Yeltsin who allowed him to be extradited from Moscow to the former DDR in a perverse BRD orchestrated show trial on his "crimes") bitterly recount.

Where to even begin? Yugoslavian regional desires? Vietnamese Doi Moi and how it emerges from Le Duan and how that stems from the differences in the north and the south's unequal development despite a common struggle? Che's writings on USSR/Cuba/Free Trade/Sugar? Defining what differs between Khrushchev or Deng(its nothing)? How soviet "social imperialism" is in retrospect clearly subordinated to American imperialism and now China repeats the same mistakes today. The eurocommunism-maoist split and how that really does derive from various European communist parties and just about every single USA communist parties revisionism, which plays out now in various rightist deviations towards what "actually exists" and from that "what is actually possible".

And of course all of this precedes the answer to why post colonial bourgeois nationalism flared up in border struggles with Vietnam and China, and now regrettably we have a china that continues many of these trends. Laos and Vietnam still at least exist as a good model of interstate relations, or much of the Soviet unions internal borders at least before capitalist restoration and the return of genocidal ambitions we see today.

not to be trite with you, this question is massive, and arguably as fundamental to communism as any other question nowadays, given its real applicability on how revisionism re-asserts itself time and time again, although its particular contours are obviously not at all limited to "who gets to own a couple islands along the amur river". No easy book to start with, but Albania-China relations is probably as good a starting point as any.