"I am on the side of the Trojans. They fought for a woman"

This refers to the Trojan War in Greek Mythology.

When the goddesses Aphrodite, Athena and Hera argued over who was the fairest of the three, Paris of Troy was asked to judge: he chose Aphrodite. She rewarded Paris by making Helen, the most beautiful woman on earth, fall in love with him. This led to the Trojan war, as the Achaeans (Greeks) tried to recover Helen for her husband Menelaus, the king of Sparta. 

The Greeks were ultimately victorious, but only through trickery.  Having failed to breach Troy's walls, they pretended to depart, leaving a giant wooden horse behind as a supposed offering to the gods.  The Trojans brought the horse inside the city walls, little knowing that it was full of Greek soldiers.

The Trojan War is the subject of Homer's Iliad and the starting point of The Odyssey. The war inspired works of literature by many other writers as well, including the Roman poets Ovid and Virgil.

The Odyssey on Book Drum