what was revealed about King Priam when he admonished his son hector?

What this reveals was that the King loved his son and wished to stop his death. Priam and Hecuba begged Hector to come back inside the walls, but he didn't listen. Even more importantly, he didn't listen to the words of his wife and son who implored him to stay with them and not do battle. His reply;

"I know the day shall come," he answered, "when holy Ilios shall perish, and Priam and the folk of Priam of the goodly Ashen Spear. But thought of him, of my mother, of my brothers, does not trouble me so much as that some warrior of the Achaians shall rob thee of the day of freedom." He stretched out his hand to the little boy, who shrunk back to his nurse's breast in fear of the bronze and the horsehair crest that nodded dreadfully from the top of the helm. Straightway Hector took off the helm and placed it on the ground. And when he had kissed his son and tossed him in his arms, he spoke in prayer to Zeus and the rest of the gods. "Grant, ye gods, that this son of mine prove foremost among the Trojans, a good and mighty king. And as he comes back from battle may many a man say of him, `A far better man than his father,' and may his mother rejoice in heart." And then he handed him back to his mother, who received him smiling through her tears, and so de-parted to the battle with words of high cheer."