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 as anyone that the Trojans are doomed to defeat, with all the terrifying consequences that will follow for his family.

Hector would like to stay home with his wife, Andromache, and young son, Astyanax, as Andromache pleads with him to do as he leaves for battle. Yet, as Hector explains to her, he cannot function as an honorable man in Trojan society if he does not fight to defend his homeland. In the ancient Greek world, a man's worth rested on his military prowess and courage. If Hector, Troy's greatest warrior, did not rise to the occasion, he would be disgraced. Further, if Troy doesn't win the war, as Hector explains, Astyanax will be killed and Andromache taken off as war booty. He feels he has no choice but to fight to defend them.

The frightening divide between Hector the father and family man and Hector the warrior is emphasized when Astyanax does not recognize his father in his armor and cries with fright at his helmet and plume. Hector and Astyanax laugh at this but also comfort the child. Astyanax's tears reveal what it as stake: war is a serious business involving suffering and costing many lives.

In showing us the tender domesticity of Hector's parting from his family, Homer gives us a glimpse of the peaceful life the men are fighting to preserve and reveals what they have to lose. The scene is especially poignant as Hector, for all his valor as a fighter, will be on the losing side and will die, bringing disaster to his wife and child.

Hector has conflicting responsibilities as a warrior and a family man, which is part of why he is such a beloved and tragic character. In The Iliad, Homer paints a picture of Hector as a worthy and righteous man. Some scholars contend that Hector is, in fact, the protagonist of The Iliad, since it focuses on his death and ends with his burial. As a brother, a prince, and a warrior, Hector is motivated to defend Troy and stand up for his brother Paris, who stole away the beautiful Helen of Sparta. He is also probably somewhat motivated by glory, which is a major theme for all of the Greek heroes. Hector never seems consumed by the need for glory, however, in part because he has much more on his mind than only gore and war.

Hector is a family man, and one of the most touching moments in the entire epic is when he takes off his helmet so that he can hold his baby son, Astyanax, without frightening him. In some ways, he is a more well-rounded character than many of the Greek heroes. These motivations—to protect his family and also to go to war—come into conflict with each other on one level, but on another more immediate level, they feed into one another. Hector is literally defending his home. He fights not only for glory and as his princely duty, but to defend his family and the ones he loves.

The original question had to be edited.  Hector's motivations as both a warrior and man of family help to illuminate his truly tragic condition.  His motivations in both realms are extremely compelling.  There is little negotiation in this collision of motivations that are equally desirable, but ultimately incompatible.  Hector's motivations are what makes him human and a character of the highest of nobility in Homer's rendering.

There are strong and intense motivations for Hector to defend his country and stand for the honor of Troy.  For Hector, these motivations are the reasons why he fights.  They provide a clarity in his action.  Hector stands for his men and the soldiers who live and die for Troy.  His motivations to honor these men and his selfless commitment to defend Sparta are immediately juxtaposed with his commitment towards Andromache and his child.  For Hector, his love of them is as pure as his love for Troy.  The position he holds as a Classical warrior is only matched by the position he has as a husband and father.  The motivations to do right in both realms is where Hector's tragic condition is illuminated.  In this, Hector becomes one of the most human characters in the work because of the equally compelling set of motivations.