In Greek mythology, Phoenix was son of king Amyntor. After a quarrel over his father's concubine he fled to Phthia, where Peleus made him king of the Dolopians and tutor of the young Achilles. In Homer's Iliad he is the old counsellor of the Book 9 embassy who fails to persuade Achilles to return to battle; later tradition sends him to fetch Neoptolemus from Scyros and has Neoptolemus bury him on the homeward voyage.
Adapted from Wikipedia, "Phoenix (son of Amyntor)" · CC BY-SA 4.0
I.Exile and tutoring Achilles
In the Iliad Phoenix's mother (later named Cleobule, Hippodameia, or Alcimede) urges him to lie with Amyntor's concubine so the old king will hate her; Amyntor curses him with childlessness through the Erinyes. Phoenix nearly kills his father, then flees Hellas; Peleus receives him like a son, sets him over the Dolopians, and gives him the infant Achilles to raise as a speaker of words and a doer of deeds.
Apollodorus, probably following Euripides' lost Phoenix, has the concubine Phthia falsely accuse him of seduction; Amyntor blinds him, but Peleus brings him to Chiron, who restores his sight. Ovid and Hyginus also list him among the Calydonian boar hunters; the Cypria has him name Achilles' son Neoptolemus ("young soldier").
II.Embassy and after Troy
Agamemnon sends him with Odysseus and Ajax to Achilles' hut. After Odysseus' offer fails, Phoenix weeps through a long speech — his own life-story, the allegory of the Litai (Prayers), and the cautionary tale of Meleager — begging Achilles to master his pride and accept gifts. Achilles refuses to relent that night but invites Phoenix to stay. Phoenix later leads a Myrmidon company, appears when Athena borrows his likeness to spur Menelaus, comforts Achilles after Patroclus' death, and umpires at the funeral games.
Sophocles and Apollodorus send Phoenix with Odysseus to bring Neoptolemus from Scyros; the Nostoi and Apollodorus say he died on the return and Neoptolemus buried him. Lost fifth-century tragedies titled Phoenix treated the father-quarrel; he is a frequent figure on early classical vases of the embassy scene, often marked by white hair. This notice concerns Amyntor's son, not Phoenix son of Agenor.