The claim that one is a citizen of the world has been attributed to both Socrates and Diogenes. If Socrates made the claim, he did so before Diogenes who as a Cynic was a follower of Socrates as were the Stoics. It was the man Socrates, though, they followed and not the creation of Plato--the character appearing in Plato's dialogues. It's said that Socrates was concerned primarily with philosophy as a guide to how to live, and eschewed epistemology and metaphysics which, alas, meant a great deal to Plato.
The idea of being a citizen of the world instead of a citizen of a city-state evidently horrified many at that time. It seemed to denigrate the city of one's birth, the significance of one's county. This was deemed unpatriotic then and is still thought to be now, particularly it seems in our Great Union. For the Stoics, however, being a citizen of the world, the cosmos (thus cosmopolitan), was something of great worth and followed from the desirability of being virtuous. It emphasized the common nature of man and fostered the ideal of a brotherhood of man encompassing the world; ideally a world which functioned according to natural law.
Those who believe in American exceptionalism sometimes think it appropriate to proclaim this fact in a rather prideful manner. We are proud to be Americans and feel ourselves in some sense better than those who are not. But pride, for me, when we apply it to ourselves, is something which we're entitled to feel when we, personally, have achieved something. We who are born Americans did not achieve that status properly speaking and what our country does isn't necessarily our personal achievement. It would seem more appropriate to be grateful we're Americans in that case, and this in turn would seem to make it less likely that we would indulge in the chest-pounding we like to engage in when patriotism is invoked. But instead we boast of our country rather as we do our favorite team in sports, which diminishes our country and I think ourselves.
But we are not alone in our pride and our belief in our superiority and exclusivity. In fact, the world seems more tribal now than it has in the past; indeed, it seems violently tribal. Religious extremism, racism, ancient grudges perceived or actual, political disagreements, nationalism, all seem create divisions among us. Curiously, the fact that the world is for other purposes "smaller" than ever before due to technological advances hasn't mitigated these divisions. It seems to enhance them in certain senses, in fact. We live in a time where we can learn most anything we want about what is transpiring throughout the world in real time, and the opinions of others are readily available if we care to discover them. Perhaps we are intimidated by this rather than enlightened.
The wisdom of the Stoics and others is in any case disregarded. It may be this is due to the fact that we resort to the most comforting, simple beliefs when confused or uncertain, even if those beliefs sanction barbarity. Anything to avoid thinking. It may be we're fundamentally irrational creatures regardless of our knowledge and sophistication. It may be we wait for a god to save us like the unfortunate Heidegger (the Fuhrer having failed him), and in the interim are willing to do anything that will assuage us.
I'm more inclined to believe that selfish concerns, the pressure of cultural and religious beliefs long ingrained in us and an unceasing desire to master or possess things which are not in our control are at fault, but must confess that I despair of this ever changing unless we take the time to train ourselves and others to think rationally and understand the insignificance of the things which dominate our conduct and desires. This training, though, may be something which can't be imposed on others in any useful manner. It would seem to be worth a try, though, as nothing else has worked in the past.
One sees why education has been considered so important to certain philosophers. How to think is something which should be taught as early as possible, but parents fear this and may not tolerate it as part of their children's education. This is because they're inclined to want their children to think and act as they do, and fear that their children won't be taught to think as their parents do, which would likely be true.
This has been recognized, and since Plato those who think they know what is best for all have dreamed of education as a process by which those being educated are dragged to the truth as it were, screaming and kicking if necessary. It's why totalitarian, fascists and other authoritarian governments insist so often that children be taken from their parents to be trained in the Right Way.
We're in trouble I fear, and the question is how and whether we'll work to get out of it. I doubt if circling the wagons is the way to go, but am having problems coming up with workable solutions.