The Gigantomachy was the Battle of the Gods and Giants. Shown on the east side. The gods in question were the Olympians, Athena’s clan. The Giants were the Earth-born sons of Gaea (Earth ) sired by the split blood of the sky-god Uranus. The people of Athens considered themselves autochthonous, that is born of the earth; the local soil. It is hard to imagine them cheering on the destruction of their earthly brothers unless the symbolism of the Gigantomachy is the victory of Order over Chaos
On the North side is the Trojan War, which is the kick off point for the great “East is East and West is West “ divide. (Plus the Athenians were the only ones not accused of atrocities the night Troy fell. Theseus’ sons were busy looking for their grandmother Aethra. )
Finally, on the North the battle between the Athenians and the Amazons. The Amazons were warrior women from the far edge of the Black Sea. If the significance of the Amazonomachy was men over women, it would be Greek women. I would suggest that in addition to Greg’s proposal that a different level of symbolism sees this as the defeat of the “Other”. Here the forces of Chaos are represented by barbarians who are women, is there any possible group full of such otherness for the Athenians
The Titanomachy, was not represented on the Parthenon. It was the war between the Olympians and another divine clan called the Titans. I don’t know what the allegorical significance would be. Suggestions?