Why does the olive tree represent Athena?

In Greek Mythology, Athena and Poseidon fought for Patronage of Athens. They decided

to have a competition. Whoever made the best gift for man kind would win patronage.

Athena made the olive tree and Poseidon made a spring. The mortals saw her gift was better. So the mortals gave her Patronage and the olive tree became one of her symbols.