Could you be more specific? The Serbs and Croats certainly hate each other because of ethnic/religious conflicts dating back to the Turks (Croats are Catholic with a Latin alphabet, Serbs are Orthodox with a Cyrillic alphabet). The predominantly-Muslim Bosnians were caught in between them during the breakup of Yugoslavia in the 1990's. The Greeks fought for a century to win their country back from the Turks and then invaded the Turkish coast itself (and lost horribly) during the 1920's. The Bulgarians (with Russian diplomatic support) turned against all of their neighbors in an attempt to gain more land during the Second Balkan War and then sided with the Central Powers during WWI against Serbia and Greece. The Hungarians (who ruled their territories rather harshly during the time of Austria-Hungary) sided with the Axis during WWII to reclaim the Carpathian Basin. Romania had a sizable part of its territory (Transylvania) ruled by those very same Hungarians. There's a large Albanian population in the breakaway Serbian province of Kosovo. As far as I know, Slovenia has avoided a lot of those problems and... Well, the Macedonians occasionally want to argue with Greece over whether Alexander was a Hellene or a Slav.
EDIT: Serbs, not Serbians.
This is a tough one, and I can literally write a volume on it if I wish. The question is broad, but I'll attempt to iron out some realities which often go unmentioned in popular narratives. I'm a specialist in Croatian history, and will talk about early issues, until the end of WW1
Regarding the Serb-Croat rift, it's important to note that there has never actually a been a conflict between the two nations. I'm speaking of course of a full-scale war between Serbia and Croatia. The hatred of which you speak stems from friction born of historic realities in multiethnic states (both defunct historic ones and modern [re]incarnations), and outstanding modern issues between Serbs and Croats as a result of a century of co-existence in the several states we'll call "Yugoslavia" for simplicity's sake. A dominant theme is the inversion of ethnic power structures as a result of the collapse of Austria-Hungary and the Ottoman empires. Unbeknownst to most, Croatia had existed as a junior partner in a dual-kingdom arrangement with Hungary since the 11th century. While ostensibly retaining all sorts of rights, Croatia was in practice almost completely subsumed into the Hungarian power structure by the 19th century. It also had on its territory a large Serbian minority, concentrated in Dalmatia and the Austrian military frontier. What is the latter, you ask? In the 17th and 18th centuries, Vienna had encouraged the settlement of ethnic Serbs along the border with the ottoman empire. They were given land, tax exemptions, and other preferential treatment in exchange for military service as border guards against Ottoman Turkish encroachments. This understandably caused friction and resentment amongst the Croatian population. By the 19th century, Hungarian administrators engaged in policies of disproportionately favouring the Serbian minority in Croatia, which was numerically too small and impoverished to pose a political threat, but was a counter-weight to the emergence of Croatian nationalism which threatened to undermine the stability of the Dual monarchy (after 1867).
With the dissolution of Austria-Hungary in 1919, Croats and Slovenes joined with the new(ish) kingdom of Serbia to form the state (and subsequently kingdom) of Serbs, Croats, and Slovenes. This became the Kingdom of Yugoslavia in 1929. The formation of the state came under strange circumstances, and the forces which coalesced and carried the impetus for it could not have been more volatile. The crux of the issue here, following the Great War, is that the two sides (Serbs and Croats/Slovenes) entered into the new state with two different historical experiences, had radically different expectations of what this arrangement would be as a result of these experiences, and were unequal in the ability to impose their will.
Croatia/Slovenia had been meager holdings of the Austro-Hungarian crown since 1527. Its nobility had grown accustomed to wheeling-and-dealing for rights and status within a larger imperial framework where they were one of many minorities. They expected Yugoslavia to preserve their rights to statehood, and be a country in which they were equal partners with the Serbs.
This was not the case. Serbia, if one is to be objective, entered into Yugoslavia in 1919 as a victorious but profoundly traumatized state. It had been nearly obliterated during WW1. Between 25-35% of its population had been decimated, depending on how you wish to factor war-related deaths. It's infrastructure, which was poorly developed before the war, was ruined in the fighting and then destroyed by retreating German, Austrian, and Bulgarian forces. Serbia had recently fought (and won) two Balkan wars, in 1912 and 1913. It had endured an altogether vicious occupation by the ottoman Turks between the 15th-19th centuries (this point is more nuanced, but I simplified it). In short, Serbia was riding a wave of three military victories (two balkan wars, and WW1), suffered a greater level of physical and population destruction in WW1 than any other country (by proportion), and emerged militarily strong. It viewed Yugoslavia as its reward for what many saw as centuries of struggle and sacrifice. The nascent Croat and Slovene ethnicities were interpreted as simply arms of the larger Serbian ethnicity, or Serbs as one of several branches of a greater South Slavic family.
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