Because the Greeks themselves held him to be so. In Book X of the Republic, Plato has Socrates speak of the admirers of Homer who said that this poet had educated Greece, and that for governing and educating men it was worth learning him and ordering one's whole life by him. When people ask who was the greatest educator of all Greece, that is the answer the Greeks gave.
In practice, Homer was the schoolbook. Children learned to read and recite with his verses, and some knew both poems by heart: in Xenophon's Symposium, Niceratus says that his father made him memorize the whole Iliad and Odyssey so that he would become a good man. From the poems they drew their gods, their virtues, their models of courage, prudence and piety, and even examples of language.
It was precisely this power that led Plato to leave him out of the ideal city. Socrates recognizes Homer as the most poetic of poets and the first of the tragedians, but admits into the city only hymns to the gods and praises of good men. The charge is one of competence: if Homer truly knew about war, government and education, some city would owe its laws to him, as Sparta owes them to Lycurgus.
The German classicist Werner Jaeger took up the formula in the twentieth century, in Paideia, where he studies Homer as the first educator of the Greeks.
On Clavis: The Iliad, The Odyssey.