Quote 1
(Hektor:)
Poor Andromache! Why does your heart sorrow so much for me?
No man is going to hurl me to Hades, unless it is fated,
but as for fate, I think no man has yet escaped it
once it has taken its first form, neither brave man nor coward. (6.486-489)
Okay, so we know Hektor is trying to cheer up his wife here, but if you were Andromache would you fall for that? So what if Hektor will only die when he's fated to die? Doesn't it still make sense for his wife to be sad whenever he dies? On another point, when Hektor says that the brave man can't escape his fate any more than the coward, what do you think would make someone want to be one instead of the other?
Quote 2
(Hektor:)
If it is true that brilliant Achilleus is risen beside their
ships, then the worse for him if he tries it, since I for my part
will not run from him out of the sorrowful battle, but rather
stand fast, to see if he wins the great glory, or if I can win it. (18.305-308)
Have you ever gotten yourself into a difficult situation just because you were afraid to admit you couldn't handle it? Sure you have. You should understand what Hektor's going through at this point.
Quote 3
(Hektor:)
Ah me! If I go now inside the wall and the gateway,
Poulydamas will be first to put a reproach upon me,
since he tried to make me lead the Trojans inside the city
on that accursed night when brilliant Achilleus rose up,
and I would not obey him, but that would have been far better.
Now, since by my own recklessness I have ruined my people,
I feel shame before the Trojans and the Trojan women with trailing
robes, that someone who is less of a man than I will say of me:
"Hektor believed in his own strength and ruined his people." (22.99-107)
This is a classic example of pride's double jeopardy. Because he was too full of himself to listen to Poulydamas's advice back in Book 18, Hektor now finds himself in a bad situation. But, for the same reason, he can't get out of that situation because he's afraid of Poulydamas saying "I told you so."