Greek city states had a national identity
Greek city states rallied under a banner to defend their city against the Persian empire.
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City state: a city that with its surrounding territory forms an independent state.
In Ancient Greece, there were over a thousand different city states , each with their own cultural identity. Athens was known for producing scientists, philosophers, and writers, whilst Sparta was famed for its prowess at warfare, and each city state had its own system of government, varying from rule by kings to democracy. However, despite their differences, these city states felt a common identity when fighting the non-Greek state of Persia, and the Greek victory was seen as a triumph for Greek culture and politics, even though what that meant specifically varied from city to city.  This suggests that nationalist identity has existed since before modern nation states, and that groups do not have to be culturally identical to feel a strong bond to one another.
This sense of Ancient Greek nationalism is very loose and was formed only in the face of the threat of Persian conquest: before that, the cultural differences between many Greek city states had caused them to fight amongst themselves. Using this as a clear example of nationalism fails to recognise that it was not strongly developed, and only emerged at a point of crisis.
This is a very specific argument drawing on the Greco-Persian Wars of 492 BCE to 449 BCE, suggesting that nationalism existed amongst these Greek city states when they were attacked by Persia.
Ancient Greek city states, despite their cultural differences, fought together against the Persians to protect Greek culture. The city states were not unified as one nation state, suggesting that nationalism came before nation states.
Rejecting the premises
This nationalism only emerged when Greece was under threat from Persia, not necessarily beforehand. City states had often fought amongst themselves.