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(Odysseus:) 'Stand as you are, girls, a little away from me, so that I can wash the salt off my shoulders and use the olive oil on them. It is long since my skin has known any ointment. But I will not bathe in front of you, for I feel embarrassed in the presence of lovely-haired girls to appear all naked.' (6.218-222)
Odysseus has no qualms about ripping off his shirt in a hall full of suitors, but he doesn't feel a little embarrassed about wandering around naked in front of girls with nice hair. (Well, to be honest, he's probably afraid that he'll end up having to fight them off, once they get a good look at his god-like physique.)
(Odysseus:) ‘Then I shoved the beam underneath a deep bed of cinders, waiting for it to heat, and I spoke to all my companions in words of courage, so none should be in a panic, and back out […].’ (9.375-377)
In the Odyssey, honor is proven by showing courage in the face of adversity; Odysseus urges his men to action on the grounds that they must do just this.
(Odysseus:) ‘But when the young dawn showed again with her rosy fingers, then I sent my companions away to the house of Circe to bring back the body of Elpenor, who had died there. Then we cut logs, and where the extreme of the foreland jutted out, we buried him, sorrowful, shedding warm tears for him. But when the dead man had burned and the dead man’s armor, piling the grave mound and pulling the gravestone to stand above it, we planted the well-shaped oar in the very top of the grave mound.’ (12.8-15)
Odysseus honors the dead Elpenor by setting up a proper burial for him. This ensures that he will not be forgotten among the living and will have respect among the dead.