Hector's position as a warrior is closely linked to his role as husband and father. In the event of a Trojan defeat, Hector knows all too well what will happen. The city of Troy will be completely destroyed and all the surviving men slaughtered, with their women and children being turned into slaves. So Hector isn't just fighting for Troy, or for himself and his own honor and glory, but for the welfare of his family, too.
Somehow he must balance his duties as chief Trojan warrior with his responsibilities as a father and husband. On the one hand, he's expected to lead by example, displaying exemplary bravery on the field of battle. At the same time, he can't allow himself to get too carried away, as this will lead to reckless acts that could easily get himself or his men killed.
So long as Hector's alive, he can act as a rallying point for his men, providing the Trojan warriors with a significant boost in morale at key moments in the battle. But the moment Hector dies, he knows as well...
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