Why did the citizens of the policies of Greece voluntarily go to the mortal battle against the troops of Xerxes?

This is due to the fact that the Persians wanted to capture the Greek city-states. In this connection, the Greeks went to battle with the Persian army, not sparing their own lives. The first big impetus for the unification of the Greek city-states against the Persian state was the battle of Marathon, where the Greeks were able to inflict their first defeat on the Persians. So the Greeks, at the head of Athens, began a struggle against the Persian conqueror. In the future, the Greeks were able to inflict several more defeats on the Persians and spread the war to the enemy’s territory.