It was dangerous for King Priam to claim the body of his son Hector because he had to go into the Greek camp all by himself. He might have been killed or taken prisoner before he ever reached Achilles' tent. Then he had no way of knowing what sort of reception to expect from Achilles himself. Achilles had been in such a rage over the death of his friend Patroclus that he drove the entire Trojan army off the field and then abused Hector's body after killing him. If Achilles' rage had not abated, there was a good chance that he would kill Priam too. Priam displayed extreme courage in going to Achilles and then displayed extreme diplomacy, intelligence, and humility in begging for Hector's body in order to give his son a proper funeral.