Why did Athena have a Spartan helmet?

Athena's helmet was not specifically Spartan, it was the helmet used by a Greek infantryman, a "hoplite" which was the backbone of all Greek polis (i.e.city states). The Hoplites of Sparta of course were the most famous because of their military superiority in ancient Greece.Mostly in time between 650-470BC.

Athena wears a helmet as in addition to being Goddess of Wisdom, she was also Goddess of a Just War.