Well, to understand his obsession, you have to understand what he ment by "keeping Yugoslavia together" or rather what he ment by Yugoslavia.

Yugoslavia was, technically, created in 1920 and it was called Kingdom of Serbs, Croats and Slovenians. Later renamed to Kingdom of Yugoslavia. Original idea came form both Serbian and Croatian intellectuals, in late 1800s and its idea was basically to have one unified stated of all Slavs living in South (east) Europe (Yugoslavija, basically translates to South-Slavs) Now, both Serbian and Croat nationalist felt that union was against their national interest. Primarily Croats felt that centralist government with Serbian King (Serbian dynasty of Karađorđević, which previously ruled kingdom of Serbia) was against Croatian national interests and with centralized government in Belgrade, they felt that it was basically a Serbian state. There were certain policies fro exapmlae of "Serbnisations" of certain regions (Macedonia and Kosovo, called Southern Serbia at that time) and basically non-Serbs felt that it was de-facto Serbian state,with King as Serbian and majority party (Serbian radical party) in government

After WW2 Yugoslavia was reborn, this time as communist federal state, divided into 6 constituent republics. This time Serbian nationalist felt that they were being cheated by this union as Serbia was divided into two autonomous regions. This was done some argue to limit Serbian power, create sense of balance and silent nationalist tensions among non-Serbs. Officially it was to give each ethic group a ruling power. However, at same time it created dissent among Serbian nationalist. But not only Serbians, Croats still felt they were dominated by Serbians, and Albanians never felt they belong in such union. So there was lot so f dissent and lock ups during communist rule, on all sides

Now, after Albanian majority in Kosovo revolted and asked to become a constituent republic. Serbian minority in Kosovo felt they were prosecuted by Albanian majority and were seeking help form Serbia. Nationalistic tensions started to emerge. Milosevic, who at time he was a president of Serbian Central Committee dissolved Kosovo parliament and basically annulled Kosovo autonomy. During his speech in Gazimestan in 1989 (Source, Milsevic speech during 600 years of Kosovo battle commemoration) he refereed to Kosovo Autonomy as "injustice done by previous leaders". Meaning, that Serbia as Republic in Yugoslavia should not have been divided into two autonomous provinces. Now this was seen as resurrection of Serbian nationalism and rise of Serbian nationalistic aspirations in Communist Yugoslavia. Democratic elections followed and each Republic suddenly had their respective nationalist as a leaders.

When Croatia expressed its desire to break away from Yugoslavia it had around 20% of Serbs at that time. Serbs in Croatia had constitutional rights, meaning they were constitutional entity. Newly elected government of Croatia abolished this status, meaning Serbs had only a status of a minority. This didn't bode well with Serbians, as they felt they were losing their rights and arguably influence. Wen Croatia expressed desire to also become independent state.. Milosevic objected to this, with his famous words "All Serbs will live in one state" . This was seen as aspiration to greater Serbia and war broke out, with Serbia and Yugoslav Army at that time aiding Serbian minority. Milosevic argued in his trail that what he meant with "all Serbs will live in one country" is that will resist for Yugoslavia to break up and had nothign to do with Grater Serbia project.

In Bosnia also, there were democratic elections where Bosnain Muslims had majority and Bosnian president was elected and they also expressed desire to break away. . Bosnian Serbs however didn't want to want to break away from Yugoslavia and opposed it. Alija Izetbeovic called in final siting in Bosnian Parliament (soruce yioutube) , called for "old Serbian democrats tradition" and implored for Serbians in Bosnia to agree with democratic wish of majority and allow break away, to which Radovan Karadzic responded with "If you do this [secede from Yugoslavia] Muslims from this region will disappear" to which Alija Izetbegovic responded with "this is exactly the reason why we don't want to be in Yugoslavia" What he ment by this was that Serbs were pushing "either you will live with us or you are against us" agenda, and living in such union was no point when only it will be "the Serb way or highway"

So, the main reason Milosevic kept insisting on keeping Yugoslavia together was that theoretically Serbia and Serbian national interest would benefit the most if such union was to continue to exist. Milosevic, arguably, used "keeping Yugoslavia together" as propaganda tool. In other words, with that he presented himself as "good guy who wants to keep Yugoslavia together" while other guys would be portrayed as baddies that want to break up the union. There was nothign inherently wrong for Serbs who live abroad, but you have to keep in mind the historical context and with nationalistic sentiments rising Serbs living in both Croatia and Bosnia felt they were losing their freedom and connection with its motherland, Serbia. So basically, they didn't; want to live "abroad".

Edit: Sources

Part of the answer lies in the fact that 1974 Yugoslav Constitution granted the right to secession to nations of Yugoslavia (Source: 1974 Constitution of Yugoslavia, Basic Principles, I). Since Yugoslav Serbs did not want to secede, Yugoslav government was legally obliged to prevent them from being forcefully seceded.

Then another part of the answer lies in the fact that this was simply supported by the population and gave him political power.

You could likewise ask the opposite question: why not? Since Serbs of Yugoslavia did not want to secede, and since they had legal basis for it, why were various foreign powers so obsessed with having Serbs be disunited and split among several newly formed countries?

(As a sidenote, you may note that Yugoslav Albanians were not a nation of Yugoslavia, but rather a national minority.)