You can't be a citizen of the world, any more than you can be everybody's spouse. Divided loyalties aren't loyalties at all.
Stuart Schneiderman [link] has this to say about it:
Somehow or other we have been lulled into thinking that we must all become idealists and that our idealism should trump our patriotism.
We have been told, by thinkers on the left and right, that America is an idea and that belief in this idea is essential to becoming a citizen. I have variously offered my view that a nation is not an idea. A nation has borders and it has citizens. Some people belong. Others do not. Belonging has to mean something more than sharing a state of mind or believing in a bunch of dogmas. You cannot belong a nation while identifying yourself as a citizen of the world.
In two columns George Friedman—the only Friedman worth reading these days—has used slightly different terms. By his lights liberal democracy cannot exist outside of a defined nation. But, he does not see liberal democracy as an ideal. He sees it correctly as a set of practices. Historically, liberal democracies replaced monarchies. They could not have done so, Friedman argues, without a strong sense of nationalism, that is a sense of belonging to a nation.
And Chateau Heartiste [link] says that when you eliminate borders, you get more borders, because it's a human thing.