Who rules this global unity? A government in Washington? London? The UN? People in different cultures want different things from their country. Just look at the US right now. Split down the middle between what kind of leadership there should be right now. And the US is fairly simple in that most people are happy to pigeon hole themselves as either liberal or conservative. On other countries things are more complicated. Ethnic groups who hate one another. Opposing Religions. Separatists. Unionists. In many countries there are separatist movements who want to split the country into smaller countries, because they don't feel like they are adequately represented in the majority.
It's a lot more complex than ditching the silly flags.