There was no real reason. It was mostly "political elites." The decision to split was decided mainly by Vaclav Klaus ( Czech), and Vladimir Meciar, (Slovak), who after proceeded to become the Prime Ministers of the new countries. Polls showed that people didn't like the idea of two separate countries and wanted it to remain one, even though there were many differences between the two countries.
Czechoslovakia was just one big country with a bunch of races. Dictator Tito kept the races together in one country but that's not what they wanted. So when Tito died they decided they wanted to separate and each have a country of their own. Though I'm not an expert on that subject, i'm sure someone else has a better answer.