What are you even talking about man. I don't know how you misinterpreted that so badly. He is saying yes I might die but if I don't risk my life you will be a slave, so I am going to fight for you:

"And tall Hector nodded, his helmet flashing: “All this weighs on my mind too, dear woman. But I would die of shame to face the men of Troy and the Trojan women trailing their long robes if I would shrink from battle now, a coward. Nor does the spirit urge me on that way. I've learned it all too well. To stand up bravely, always to fight in the front ranks of Trojan soldiers, winning my father great glory, glory for myself. For in my heart and soul I also know this well: the day will come when sacred Troy must die, Priam must die and all his people with him, Priam who hurls the strong ash spear . . . Even so, it is less the pain of the Trojans still to come that weighs me down, not even of Hecuba herself or King Priam, or the thought that my own brothers in all their numbers, all their gallant courage, may tumble in the dust, crushed by enemies — That is nothing, nothing beside your agony when some brazen Argive hales you off in tears, wrenching away your day of light and freedom! Then far off in the land of Argos you must live, laboring at a loom, at another woman's beck and call, fetching water at some spring, Messeis or Hyperia, resisting it all the way — the rough yoke of necessity at your neck. And a man may say, who sees you streaming tears, 'There is the wife of Hector, the bravest fighter they could field, those stallion-breaking Trojans, long ago when the men fought for Troy.' So he will say and the fresh grief will swell your heart once more, widowed, robbed of the one man strong enough to fight off your day of slavery. No, no, let the earth come piling over my dead body before I hear your cries, I hear you dragged away!”"

> Achilles gets mad about not getting his fair trophy share

He's mad because he is camped out on a beach for a decade helping Agamemnon, which he has no obligation to do, and Agamemnon steals his sex slave for little reason and tells him to fuck off. Achilles then refuses to war for this guy, very reasonably.

I think you must have skimmed this book very rapidly because you seem to not understand what you read.