Why is the death of Ctesippos, one of the pretenders, by Philoitios, the cow herder, an example of irony?
In Book 22 of Homer's Odyssey, Odysseus has strung his bow, revealed his true identity, and has begun slaughtering the suitors of his wife Penelope. Odysseus is assisted in this battle by his son Telemachus, his swineherd Eumaeus, and another of his servants, Philoitios (also spelled Philoetius).
In the course of the battle, Philoitios "skewered Ctesippus through the chest". There may be multiple levels of irony here. On one level, I suppose it is ironic that a lowly servant should kill a nobleman. On another level, there may be some irony in having a cowherder kill a man whose name means "possessor of horses." It may also be ironic that Ctesippus, who had earlier thrown a bull's hoof at Odysseus, is now killed by a man who herds livestock. Another level of irony could exist in Philoitios' remark that the spear through his chest is "a guest gift, a match for the hoof" that Ctesippus threw at Odysseus when he was disguised as a beggar.
So, I would say that a number of different possibilities for irony could exist in this brief exchange.