Well, it's the obvious. We love Balkan people.(not all of them

) We consider Bosnians, Albanians, Kosovans and even Macedonians and Hungarians(this is another topic) as our brothers.
But I'd like to go a little bit back in the history to explain the bonds between the the Turks(not as the etnicity) and the Balkans' people.
That's mainly because of the Ottoman policy. Unlike the former turkish empires, Ottomans didn't care about the etnicities much and let lots of people from other etnicities, into it's government system to have high positions in the palace, military or religious states. A form of this was the "devşirme system", which is basically finding talented or bright christian boys, especially from the Balkans, taking them from their families(forcibly, sometimes), converting them into Islam and training them into the leadership positions in different areas, even to the top of the empire! One of the main reasons to executing this system was for stating that it's not an empire which only belongs to the turkic nobles but also to 30 different etnic citizen groups of the empire. It was also preventing the fights for the throne between the turkic nobles. (Before Ottomans, tens of turkic empire collapsed because of that throne issue.) With in the time, this system started to work well, because people were themselves wanting to go into the Palace.
Anyway, in the first place, the ottomans have always considered the Balkans as too important, because their ultimate dream was conquering the whole Europe hehe

. They've considered the Balkans as the main lands of the Empire and the whole anatolia was just the hinterland. At the end they couldn't managed to go beyond the Vienna but they've stayed at the Balkans for more than a half millennium. I think it's enough time to have very very strong bonds with those lands and those people.
There have always been many important turkish people who have Balkans origins, in the Turkish history. Several Sultans, several presidents, tons of politicians and military people, scientists, artists, athlethes, etc. Of course most of them have ottoman-muslim origins but there've been even Christian-Balkan origin turks who gave lots to the turkish history. Even in this modern times, there are hundreds of thousands turks with balkan origins live in Turkey and enrich the country.
Ironically, they have a huge influence in our basketball too, probably thanks to their tallness genes. Hedo Türkoğlu and Mirsad Türkcan(who is the best european rebounder ever) are just the most known examples.
Now finally if we come to the actual subject, Slobodan Milošević...
We used to call him "Kasap" which means "The Butcher", obviously it's in the meaning of "a murderer", "a human butcher". He was one of the biggest war criminals of the history as well as being one of the biggest idiots. He literally destroyed a hell of a country(the old Yugoslavia) single handedly. His idols were probably Hitler or Tito(their old dictator) or Mao etc... He did hell of a job murdering and massacring thousands of innocent people with his another super idiot crony Radovan Karadžić, both in Bosnian war and Kosovo war. I compare him as the modern day "Vlad the Impaler". Monster or anything but a human being.
I remember very well those days, from early 90ies(my childhood) with Bosnian War, to 1999(I was 16) the Kosovo War, to 2001 Milosevich's getting arrested, to 2006 his death in his otel-prison room in Lahey, and to 2008 Kosovo's independence... Turkey and turkish people always been supporter of Bosnia and Kosova these years, I remember Friday Sermons which are telling the situations of the poor people over there and telling to pray for them.
Turkey was also struggling with the pkk terror those years and the Iran-Iraq war next to her had just finished in 88 and there was the Gulf war rigth after that in again early 90ies. So we were all ourselves close to the war and because of this we've always been following what the hell is going in the world, and thus my and my olders' generations all know about KKO(UÇK) and Bosnian and Kosovo wars and their struggles.
Anyway, that monster never been judged accordingly nor duly, that's Europe's one big shame, to me. He then died in his 64-65, in 2006, is likely in the hell now.
So that's why we hate him, we love our brothers over there, and we hate him because of his crimes against the humanity.
And there is just one more reason to me... If he weren't, there may be still a Yugoslavia, so that flopper Spanish team couldn't dominate the european basketball.
