Historians have now dug up enough facts to believe that something like the Trojan War may have really occurred. However, the story of how it began and what started it is part of Ancient Greek mythology. We learn most of what we know surrounding the myth of the Trojan War from the Ancient Greek epic Cypria by Stasinos of Cyprus who predated Homer.
In Cypria, we learn that quarrels amongst the gods led to the war, and it is the idea that the start of the war was rooted in the actions of the gods that makes the war a myth rather than a legend. According to myth, the war began with the story we refer to as "The Apple of Discord." The sea-goddess Thetis, Achilles' mother, married the hero Peleus, the father of Achilles. Unfortunately, Eris, the goddess of discord, was not invited to the wedding. Out of rage, Eris catered to the Greek pantheon's sense of vanity by throwing a golden apple onto the banquet table and saying that it belonged to the goddess that was the most beautiful. Naturally, Hera, Athena, and Aphrodite all challenged each other for the apple. Zeus decided the vain goddesses needed a mediator and chose Paris, the prince of Troy and the most handsome mortal man alive, to judge which goddess was the most beautiful. Each goddess decided to bribe him to turn the contest in the goddess's favor. Hera bribed him with power; Athena bribed him with wealth; and apparently Aphrodite offered the most tempting bribe--the most beautiful woman in the world as his bride. Paris, also guilty of a great sense of vanity, accepted Aphrodite's bribe and chose her as the most beautiful goddess. In return, Aphrodite gave Paris the promise of Helen as his wife, the world's most beautiful woman. The problem was that Helen was already married to King Menelaus, king of Sparta, also known as Mycenae and referred to as Achaea in the Iliad. But Helen's known marriage could not stop Paris's vanity, who soon sailed to Sparta to whisk Helen away from Menalaus. Naturally, when Paris refused to give Helen back, Menalaus declared war on Troy to win her back. Hence, according to legend, the Trojan War was started by the feelings of vanity, conceit, and arrogance that dominated the gods and goddesses of the Greek pantheon as well as Paris.
Throughout the Iliad, Homer paints Paris as a very vain, dishonest, and conceited man. We can especially see his vanity and conceit named when his older brother Hector upbraids him for shrinking from fighting with Menalaus in hand-to-hand combat in Book III:
Paris...evil-hearted Paris, fair to see, but woman-mad, and false of tongue, would that you had never been born, or that you had died unwed. Better so, than live to be disgraced and looked askance at.
Homer's interpretation of Paris shows us just how much Paris's vanity and conceit played a significant role in starting the war.