Why haven't they been able to live together as one country? What are the reasons for their bitter and bloody feuds? Since when did these divisions exist?
Yugoslavia, was a country which existed from around 1918, until 1991. It was a country which lasted nearly 75 years and its longevity was nearly identical with the lifespan of The former Soviet Union.
The name, "Yugoslavia", meant, "Land of the South Slavs"; that is to say, a unified country of similar Slavic peoples who live South of the Alps. The present-day countries of Serbia, Croatia, Bosnia, Slovenia, Montenegro and Macedonia/ ("FYROM"), were the member states of the former Yugoslavia during the above mentioned years. They were and are the majority of independent South Slavic countries-(before the creation of Yugoslavia and since the break-up of Yugoslavia).
The ethno-racial, as well as ethno-linguistic differences among the various peoples of the former Yugoslavia were minimal; though the religious and sectarian differences were significant. Serbs are Eastern Orthodox Christians, Croatians are Roman Catholic Christians and Bosnians are Muslims-(Sunni sect). The Yugoslav Civil War of the 1990's, pitted each of these above mentioned ethno-religious groups against each other. These religious and sectarian divisions had existed for centuries-(primarily since the days of The Ottoman Empire). However, part of the establishment of Yugoslavia, was the anticipation of ending or attempting to end these historically prolonged feuds, in exchange for a united South Slavic land-(and as the Cold War progressed, a united South Slavic Communist land, ruled by its Dictator, Marshall Tito for over 30 years).
But, with the collapse of worldwide Communism between 1989-1991, which culminated with the implosion of the 75 year old Soviet Union, the already fragile country of Yugoslavia, was also imploding and moribund ancient hatreds were now reactivated, leading to a brutal 4 year civil war during the first half of the 1990's.
The Yugoslav Civil War, was primarily, a religious civil war-(not so dissimilar from the earlier Lebanese Civil War, which raged for 15 years). It was these very old religious differences connected with passionately strong regional and national identities which led to the break-up of Yugoslavia and the subsequent establishment of the above mentioned independent South Slavic countries-(as well as an additional semi-autonomous Serbian state within greater Bosnia). In other words, the end of Yugoslavia, was ultimately rooted in religious irreconcilability.
It is a complex issue, for which there is no simple answer.
Yugoslavia was once described as country with two alphabets (Latin and Cyrillic), three religions (Catholic Christianity, Orthodox Christianity and Islam) and four languages (Macedonian, Slovenian, Croatian and Serbian). And you want to make a country out of that? However, given that Croats and Serbs can understand each other, it is debatable whether they each speak different languages or dialects of the same language.
The general area that was once Yugoslavia was the boundary between the eastern and western Roman Empires - an immediate source of division.
Culturally, there were five groups of people: Slovenes, Croats, Serbs, Macedonians and Muslims. Culture and language were additional sources of division as was language.
The history of rule and governance of the region is complex.
Ultimately, each group wanted to be the master of its own destiny, without interference or dominance from anyone else.