2 reasons : war and imperialism.
For a few hundred years Greek cities were military powerhouses thanks to hoplite tactics and trireme techniques, which allowed them to conquer territory all over the mediterranean. Later on the Roman were greatly inspired by greek culture and conquered and influenced most of Europe. And western European countries, influenced by Greek and Roman culture, especially after the Renaissance, went on to colonise large parts of the world.
In addition, you and I most likely coming from western culture, are influence by ethnocentric history: the way we teach history is biased towards our own origins. Chinese or Japanese history books tell different stories.
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