Why does Bosnia even exsist as a state?
Historical accident. One could ask the same question about Belgium, Austria, Iraq, Jordan, Canada, most of the Central American and South American republics, and most of the countries in Africa.
The Bosnian Muslims and Bosnian Catholics don't want to be part of Serbia. The Bosnian Orthodox and the Bosnian Muslims don't want to be part of Croatia. The Bosnian Orthodox and Bosnian Catholics, for the most part, would rather be part of Serbia or Croatia, respectively, than under the Bosnian Muslims. The previous set-up was no decent solution. The current set-up is no decent solution. There is no good solution.