Iliad 7 opens with Paris/Alexander returning to the battle alongside Hector. In Iliad 3, the duel between Menelaus and Paris had been unable to bring an end to the war, so in Iliad 7 another attempt is made to bring the fighting to an end. With this duel, however, it appears that only the fighting for that day will come to an end. Thus, Apollo says,
it would be best by far to end this day of strife and conflict. Let them fight another day with Ilium at issue... (A.S. Kline translation)
In Iliad 7, Athena, who favors the Greeks, and Apollo, who favors the Trojans, decide to inspire Hector to challenge on the Greeks to a duel similar to the one fought by Paris and Menelaus in Iliad 3.
This divine inspiration is transmitted to the mind of the Trojan Helenus, who "divined in his mind this plan, in which the immortals had concurred" (A.S. Kline translation). Helenus relays this plan to Hector, who is happy to issue the challenge since Helenus also tells him that the gods have declared that "it is not your fate to die, your time has not yet come."
Thus, Hector realizes that he could bring some end to the fighting and he could also remain alive.