As he heads off out to battle, Hector knows what's at stake. If Troy should fall, then all the men will be wiped out and the women and children sold into slavery. As Hector has a wife and son, he's especially aware of the disastrous consequences that will follow hot on the heels of a Trojan defeat.
Still, he must be positive. And so, before entering the fray, he offers up a prayer to mighty Zeus, imploring him to make his infant son Astyanax chief among the Trojans, not less excellent in strength than himself, and that he will "bring home the blood-stained spoils of battle and bring joy to his mother's heart."
In his prayer to Zeus, Hector is expressing the martial values of ancient Troy, the exact same values shared by their Achaean enemies. And yet those very same values have led to the current situation, where Astyanax is in real danger of ending up being killed or sold into slavery with the fall of his native city.
Hector seems to have no real understanding of the irony here. He's lived by these martial values all his life and is prepared to die by them. What's more, he's prepared for his son to follow his example, come what may.
Further Reading
In Book 6 of the Iliad, in one of the few scenes centered on personal relations between husband and wife, Hector, who is usually stationed on the plains outside Troy, makes it back into Troy's citadel to meet his wife, Andromache, and their son, Skamandrios (also, Astyanax). Although this is not the last time they will meet (they will meet in Book 7), their meeting has the feeling of a last meeting.
After Andromache reminds Hector that his role as Troy's chief defender will result in his death, which will leave his wife and son to the mercy of the victorious Achaeans, Hector turns to Skamandrios, who reacts to his father—because Hector is still dressed in his armor and plumed helmet—with horror. Skamandrios's reaction is important in two respects: first, the infant's fear is completely realistic in that Skamandrios cannot be expected to recognize a fully-armored warrior; second, the scene reminds the listeners and readers that the war is an ever-present reality for Hector and Andromache.
At this point, Hector takes off his armor and helmet, takes Skamandrios in his arms, and, as any father would, kisses his child and "rocks him in his arms" before praying to Zeus that Skamandrios will succeed Hector as the Trojans' greatest warrior:
. . . grant that this my child/may also become, like me, renowned among the Trojans,/my equal in strength, and rule with might over Ilion; so/one day may someone claim: "He's far better than his father." (6:476-479)
One can reasonably argue that, at this point in the war of attrition, the Trojans, especially a warrior like Hector who has seen his men die every day, should have concluded that the Achaeans would eventually be victorious. However, it is equally...
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reasonable to assume that the Trojans believed they could win this fight, which has already consumed ten years and has no signs of concluding with either a Trojan or Achaean victory. Hector's prayer for Skamandrios, then, is what we would expect a Bronze Age warrior king to make for his son: exceeding his father in reputation as a warrior and continuing to lead Troy. It would simply not have occurred to Hector to pray for anything less for his son.
There is a beautiful scene in The Iliad when Hector is about to go off to battle and his wife tells him that, if he were to die, she would rather be dead herself—her life will not be worth living. Hector tells her that he too has thought about this, but he knows he would be unable to look at the other Trojans if he shirked battle. Moreover, he wants his wife to be remembered as the wife of a brave warrior, particularly because he knows the Trojans will likely be defeated and she will be judged by his deeds. He then turns to his child, Scamandius—known as Astyanax—and offers a prayer to Zeus. In it, he asks that his child should be "even as myself"—that is, chief of the Trojans. He asks that the child should be judged better than his father, that he should rule Ilius, and that he should make his mother proud with his brave deeds.
At the most critical point of "The Iliad", when Hector knows that he and the Trojans are going to lose, he offers a prayer to Zeus in honor of his child, Astyanax. He knows that with a Troy loss, the women will be made slaves or worse, and the children will never have a chance to live a free life. Hector's prayers, as he embraces his wife and son, are for his son to be a better and more glorious warrior and eventual king than he, Hector, could ever be. This prayer is also offered to Zeus as a means to eliminate the pain Hector feels out of the agonizing choice he has to make. On one hand, Hector feels absolute loyalty to his kingdom, his father's throne, and the citizens of Troy. Due to this, he has to fight. Yet, he is a devoted man to his family, his wife, and son. He can't bear the thought of leaving them, and the certain and imminent death that awaits him is too horrific to even ponder. Hector is poised between desire for his family and duty to his country, set against two equally desirable, but ultimately incompatible courses of action. He has to choose not between "good" and "bad", but between "good" and "good", making his choices all the more painful. There is no way out of this intestinal agony, and he offers his prayer to Zeus as a desperate way to avert the pain in both his predicament and his fate.