Socrates said that he was not an Athenian or a Greek but a citizen of the world.
Everything the man did made an impression. After all, he was willing to die for his philosophical beliefs. So it's not surprising that this statement, too, caught on and changed the Greek world.
After centuries of on-and-off civil war, Greece was almost ready for this idea. Certainly the Greeks needed some alternative to politics as usual, but they didn't quite realize it. The Greeks still had another half-century of civil war to go before they would exhaust themselves with the old idea of parochial patriotism, so when Socrates presented this radical idea, most Athenians wrote it off as just another crazy, provocative statement from crazy old Socrates.
Not everyone ignored him, though.
At least two of his students, Plato and Antisthenes, heard him and were inspired.
Antisthenes, who should be much better known than he is, was the teacher (whether directly or indirectly is unknown) of Diogenes of Sinope. Diogenes was a philosophical troublemaker and one of the founders of the philosophy known as cynicism - which beware! does not mean remotely what you think it does (it's a reference to dogs, for obscure reasons, not to sarcasm or sneering or pessimism).
Diogenes took Socrates's words to heart. He coined the term cosmopolites - the source of our word cosmopolitan - to mean a citizen of the world and, he tried his hardest to live his life that way. He became a living example of a man who could and did transcend parochial loyalties, who gave his loyalty to the whole cosmos.
If Diogenes did it, we can do it.
He transcended his parochial loyalties to a place. We need to transcend our parochial loyalties to any one worldview so we can give our loyalty to the cosmos of ideas.
We have been philosophically parochial. We must become philosophically cosmopolitan.