Thetis (Mom) attempted unsuccessfully to make her son immortal.  There are two versions of the story.  In the earlier version, Thetis anointed the infant with ambrosia and then placed him upon a fire to burn away his mortal portions; she was interrupted by Peleus, whereupon she abandoned both father and son in a rage.  Peleus placed the child in the care of the Centaur Chiron, who raised and educated the boy.

In the later version, Thetis held the young Achilles by the heel and dipped him in the river Styx; everything the sacred waters touched became invulnerable, but the heel remained dry and therefore unprotected.

Achilles became involved in a bitter quarrel with his commander-in-chief, Agamemnon, over the concubines, causing the young hero to withdraw from the fighting.  When Agamemnon sent Nestor, Odysseus and Ajax, to entreat him to return to the fighting, his pride and bitterness made him to stubbornly refuse.  His pride, however, caused him to lose his beloved companion (and lover), Patroclus.  Sufficiently pissed off, he returned to combat, avenging his friend by killing the Trojan champion, Hector.