In short, ethnic spoils and tensions.
In long, well, ethnic spoils and tensions but with history!
There are couple of countries in Yugoslavia that comprised it - Slovenia, Croatia, Serbia, Montenegro, Macedonia, Albania, Kosovo. Albania and Kosovo are the same with respect to ethnicity and so are Serbia and Montenegro - up until a while ago they were one country aptly named Serbia&Montenegro. Slovenia and Macedonia are the most unique, in a language sense - Serbs and Croats understand each other (heck, I can understand Serbian language better than some obscure Dalmatian dialects) pretty well. Keeping with the thesis of narcissism of small differences, the crux of conflict were Serbs and Croats, with other countries being there. Slovenes and Macedonians just declared independence and rest of countries were basically "oh, okay I guess". And the crux of the Serb-Croat conflict goes back to (ethnic) tensions persisting in socialist Yugoslavia, which goes back to (ethnic) tensions persisting during the World War 2 (but not really), which go back to ethnic tensions during the Kingdom of Yugoslavia, which go back to (IMO) abject failures of Croat nationalists during the pre-WWI era. There's a bit of Islam peppered into the story, in a way that a modern person (whose exposures to Islam are confined to MENA ethnicities in Western countries) might find very weird. So to begin the story:
(For the first part of the story, when I say nationalist, think leftist)
The crown of Croatian kingdom was held by Hungarian king, formal title was the "Lands of the Crown of Saint Steven (Istvan for Hungarians, Stjepan for Croats)", and Hungarian king was also the emperor of Austria, in a quite a mixture called Habsburg monarchy or Austria-Hungary, or something like that. The point was that Croatian statehood, which existed in personal union with Hungary was never in question, just its sovereignity (therefore its statehood). The status of Croats under Hungarians was...mixed to say the least, on one hand you had Magyarization (Magyar is what Hungarians call themselves) and oppressive ban (Croatian viceroy) Khuen Hedervary and on the other hand you had Croat national hero Josip Jelacic break a couple of Hungarian nationalist. Personally, Croatia only prospered under Habsburg rule, and desecration of Austrian Empire, the monarchy in general, was one of the worst moments in Croat history - may Woodrow Wilson burn in hell for it. During this era, three factions of Croat nationalism were born. First one was Illyrians, who sought to manufacture ethnic unity of Croats in Austria Hungary, then ethnic unity of all South Slavs under the moniker of Illyria which was an ancient Roman (and pre-Roman) province. Frankly, this makes as much of sense as all black people in USA trying to unite under one banner, only to attempt to unify with all black people in Canada, ... and call themselves Cherokee. From Illyrianism, or even opposed to it, came Yugoslavism which would unify all South Slavs (Jug meaning South, and written Yugo for the leetspeek cred). Ironically, founder of Yugoslavist strain of thought was a bishop, who wanted a Yugoslav Monarchy - and the irony is double because Kingdom of Yugoslavia was horrible, and subsequent Yugoslavia was a socialist state. The third strain, was the one of Ante Starcevic, also known as "Father of the Nation". It's basically bog standard liberal-nationalist version - you have a state, preferably democratic ("not a republic, but parliamentary monarchy" wink wink) of all Croats, separation of Church and State, etc. His phrase "Bog i Hrvati" (God and Croats) was a leftist proclamation that meant that there is no intermediary between God and Croats - it was later coopted by Croatian nationalist (now think right wing). Oh and he considered Slovenes and Serbs to be Croats in denial (the denial of ethnic identity will be a major plot point), with Muslim Croats being the most ethnically "pure" Croats.
(After World War I)
After the WWI, after the criminal Woodrow Wilson dissolved Habsburg Monarchy, the South Slav countries were shoved into State of Slovenes, Serbs, and Croats. This State was then merged with Kingdom of Serbia to form Kingdom of Slovenes, Serbs, and Croats. Peasant Party of Croatia opposed such a move. The head of Peasant Party of Croatia was assassinated by member of Serbian Radical Party - the assassin enjoyed luxurious house arrest with three servants (until Yugoslavian communists executed him). King of Yugoslavia then used this as a pretext to abolish the constitution and form a dictatorship. This soured the relations of Croats and led to the formation of Ustashe, which were still nationalists opposed to monarchy so still leftwing. More on them later.
(WW2)
WW2 in Balkans is one of the most confusing events, because so many things just defies common sense, and really subverts you expectations.
It's very well understand that Hitler's scientific racism (ethnicism?) was more or less post hoc rationalizations. When Kingdom of Yugoslavia rebuffed him for alliance (in a stroke of either brilliance or arrogant stupidity), he hastily fixed "Serbs are actually wandering Goth tribe" to "Croats" and he offered Ustashas a puppet state called Independent State of Croatia (NDH). But Croatia has Dalmatia, which Italians wanted, and NDH ceded its rich provinces to Fascist Italy. This, plus a lot of Ustasha mismanagment and cruelty, plus a nascent Communist movement, really soured NDH. Frankly, as someone who is both nationalist adjacent and has sympathies for fascism, NDH was a failure of an ethnic state, failure of an ideological state, and any who unironically support NDH today (which due to Yugoslav Wars, are not that uncommon) are simply retarded. And as someone who is more opposed to communism than fascism, I must admit Yugoslavian communism of 1940s did more to advance nationalist self-determination (as well as add certain parts of Italy). Really bizarre.
In opposition to NDH, both as a fascist creation (that it failed to embody the fascist principle of autarky doesn't make it non-fascist) and horrors of vengeful Croat fascists (now we come to a point where if you hear nationalist, think fascist), Communist movement (partisans) was created with the express goal of "liberation". Now Serbian fascists (Chetniks) who were de facto resistance to Ustashas, became only de jure resistance, only to be supplanted wholly by Communists after the Allies started negotiating with Tito. Failure of Ustashas to deal with Partisans, or Partisan's tenacity, led to Ustashas (Croat fascists) and Chetniks (Serbian fascists) living in a de facto alliance. The situation became extremely bizarre - imagine if the more extreme of Israel's population made an alliance with Hamas in order to root out joint Israel-Hamas Communist movement. How do different auth-rights coexist? Not very well. You can find memos by Chetniks to daddy Nazis complaining that Ustashas are mocking them ("showing their tongues") and may Uncle Adolf please spank them because we're all in this together. On the other side, it would be customary for one side to commit atrocities towards people of the other side, instead of actually armies of the other side, in a form of impotent and cowardly display of nationalism. My own great grandfather was gang pressed into Ustashe, and when Chetniks massacred his village Ustashas refused to go after them. He then switched sides to Partisans, who did.
The story basically ends here. Yugoslavia remains the only country to liberate itself during the WWII. And if you support the NDH (in other words, you're clinically retarded), NDH remains the last European Axis power never to surrender.
(Socialist Yugoslavia)
If the mess of WWII was confusing, we now return to our own bog standard ethnic system.
Socialist Yugoslavia was a communist creation. But it wasn't a Soviet creation. Formally Socialist Yugoslavia belonged to Third World when that phrase meant neither Western oriented nor Soviet oriented. This meant that it could milk both sides for the money, which it did. Yugoslavia was economically propped by Western loans. Since Soviet orientation could be interpreted as Russians flexing hard on their Western cousins by proxy, there was innate resistance, and therefore there was oppression. This wasn't the case in Yugoslavia, and while there was political censorship, it was used to curb Stalinism. Initially.
But slowly, ethnic tensions slowly asserted itself. Problem was that Croat were second largest population in Serbia, Socialist Republic of Croatia wasn't ethnically pure within its borders, and Croats were culturally similar with Serbs. Furthermore, Slovenia and Croatia were part of Austria-Hungary, and were significantly more economically advanced than rest of Yugoslavia. This disparity would persist, and persists to this day. Nevertheless, certain Croat communists started noticing publicly that there is a net flow of funds towards Serbia and from Croatia, as well as overrepresentation of Serbs in positions of power. Certain lowkey changes like certain Serbian linguists insisting that Croatian is a dialect of Serbian provoked ethnic tensions. The situation resulted in what is known as "Croatian spring" where nationalist sentiments flared up. While the main perpetrators were imprisoned and censured, certain demands were granted. Most notable of those is the constitution of 1974, which granted more autonomy to individual republics, and which sowed the seed for casus separati.
(Breakup)
After Tito died, and communism was kinda shown to be an abject failure of economic mode, situation once again flared up. Croats and Slovenes wanted to preserve their relative autonomy, seeing more value in independence than taking orders from centralized Serbian regime. Slovenes (historically and currently the most civilized and developed of all South Slavs) accused Serbs of wanting Greater Serbia parasitically sucking them dry, Serbs accused Slovenes of undermining brotherhood and unity. But money's probably fake too, and it wasn't economic situation that caused (only worsened) the breakup. Yugoslav constitution of 1974 gave republic more independence (some saw there a legitimate ability to peacefully secede) but it also granted certain autonomy to Vojvodina and Kosovo, which were provinces of Serbia. Now Kosovo was ethnically Albanian, but part of Serbia. Milosevic, Serbian communist leader, famously proclaimed "Nitko ne sme da vas bije!" in support of Serbian minority living in Kosovo. This triggered alarm bells in Croats and Slovenes - a figure of authority in one major country promising protection to his own ethnicity in one minor country? Milosevic went on to consolidate Serbian power in Kosovo, Vojvodina and Montenegro. In response to than naked display of power, communist leaders of Slovenia walked out from the final Congress of the League of Communists of Yugoslavia, followed by communist leaders of Croatia. First multiparty elections were held, and communists in Croatia and Slovenia failed to win the election. This marks the end of old-school communists who had nationalist sympathies (or, were realistic enough to not ignore ethnic implications) - Yugoslav People's Army of 90s had nothing to do with YPA of 40s, it was now Serbian nationalist wearing its skinned face.
True to their word, nationalist (democratic) parties of Slovenia and Croatia declared independence. Slovenes seceded and so did the Croats. YPA entered Slovenia, Slovenes reacted, there was a minor war, Slovenes fully seceded. The result was that multi ethnic YPA was being increasingly less multi, with many demoralized Croats and Slovenes and Bosnians seceding. This left YPA consisting only of Serbian men. Here is where problems began to occur. Croatia harbored significant Serbian minority, and Serbian minority was concerned that NDH will repeat itself. Croatia also harbored significant majority of Croats who were concerned that Kingdom of Yugoslavia will repeat itself. Serbian minority began blocking roads in the so called "Log Revolution", and various Serbian enclaves in Croatia declared independence, asking Serbia for support. Certain officers like Josip Reihl-Kir (Croat) tried to ease the tensions - he ended up being killed by his own side.
YPA then entered a city on the border of Croatia and Serbia, then proceeded to displace Croat population, and the war started in full. The said war was a full own ethnic barrel with an added constraint of semi-interested political bigshots (USA mostly) who had one line that you shouldn't cross - and that's genocide. Except ethnic tensions and genocide go together, so the whole idea was genocide, but without being caught. Croats ended up winning the war with two military operations, operation Bljesak (Glimmer, Flash) and Oluja (Storm) by recapturing all Serb controlled teritories within its border. Ethically, both operations were morally clear with minimal civilian casualties (significantly less than you would expect in this kind of war) and war crimes, especially when you compare it to world wars or dalliances in Middle East. Ethnically, the Serbian population fled their homes, fearful of the retaliation of Croats. There is some controversy, with Croat side claiming that Tudjman (president of Croatia) explicitly said that they (civilians) don't need to fear retaliation, and that government will help them rebuild their homes, with Serbian side going "c'mon, really? We're not falling for that one". There wasn't a genocide because they fled because of the implication of genocide. Wink wink. The end result was the same - ethnical purification of Croat lands.
(Lessons)
There's a couple of lessons to learn from Yugoslavia. First one is that if you cannot have a multiethnic country, you won't have a multiethnic country. Second one is that if you cannot have a multiethnic country without external economic help and politically authoritarian regime, you cannot have a multiethnic country. Third one is that main tensions that form ethnicities aren't disparity in economic prowess or something like that, but excessive charity to the in-ethnicity and diminished charity to the out-ethnicity - if you find yourselves justifying your group doing something but villifying the other group doing that same something, you're already there. Fourth one is that the point three is a cooperative process - once you start, you'll find it hard to stop. Fifth is that if measures must be undertaken very late in the game, don't do them half way - constitution of 1974 enabled nationalist who saw in it a legitimate way to secede, but the oppression of 1971 (the Croat Spring) gave them a reason to succeed, so it's either tyranny with blood soaking the streets, or peaceful secession. Sixth is that survival will be more important than ideological commitments - during the war, many Croat communists explicitly expressed support for fascist ideals, which resulted in formation of brutal and fascist paramilitary HOS. Seventh is that survival will be more important than common decency - the said HOS brutalized civillians (my father said that "grass didn't grow where they went") but if there's going to be murderers and rapists, better that they're your own murderers and rapists.
To add in, many (right wing) Croats feel slighted by Western response. There's the bog standard cry of how Western government tried to break us up because communism is just so powerful. This is usually cry of Yugonostalgics. The truth is the opposite - they tried to prop Yugoslavia up. They knew, as did anyone with half a brain, what is going to happen - Croatia and Slovenia don't want parasites sucking them dry, let alone commanding them, and minorities in said countries very much love preferential treatment. Plus, if you think Balkan powder keg needs a Western fuse you seriously underestimate (overestimate?) Balkans. Similar to thinking British/USA/SSSR colonialism lit various tensions in MENA and SSA. But Croats and Slovenes resent inaction of Westerners to atrocities committed in Vukovar (the city at the border) and constraints imposed on then. Furthermore they resent bombing of Serbia, which came as not as result of atrocities committed against them (Croats mostly) but as a result of atrocities committed against Muslim populations of Kosovo and Bosnia.
Luckily, right wing nationalist party that formed the country is sycophantic to Brusselles regime, so any resentment against European Union in the form of Euroscepticism is very very fringe. And frankly, due to communist mismanagment, population is very poor - the base pay is very very low (an average Mottian probably makes in a day what I make in a month), and the roughly 40% of my paycheck goes to prop pensioners (who retired early) and healthcare system (which I cannot use). Price of property is absurdly high with Split being third most expensive city in Europe, and borders are very porous (no commie guards ready to shoot at you). The young do not form families in their early 20s, and they have no reason to stay, and therefore they don't. The result is massive brain and brawn drain towards Western Europe - for Muslims the promised land is Mecca, for Bosniaks the promised land is Minchen, who are more than happy to accept basically white people who do not explode as much as their darker skinned brothers (we explode, dont worry).