immortality
Calypso offers to make Odysseus immortal and forever young if he will stay with her on her island. Odysseus respectfully refuses her offer.
Calypso offers immortality to Odysseus
Hermes, the messenger god, tells Calypso that Zeus has ordered her to offer Odysseus his freedom. If she does not do this then her whole island will sink to the bottom of Poseidon's oean.
Money
In book 5 of the Odyssey, Calypso offers Odysseus immortality and eternal youth if he agrees to stay with her on her island forever. She promises him a life of luxury and pleasure if he chooses to remain with her as her immortal consort.
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Odysseus rejects Calypso's offer because he is homesick and wishes to see his wife Penelope, his child, whom he has never seen, his parents, and his home once again.
Calypso does not offer predictions for Odysseus, instead forcing him to remain with her as her lover even though he wanted to return home to his wife. He receives a prediction from Tiresias who advises him troubles are to come and he will lose all of his companions.
Odysseus stays with Calypso and Circe due to the allure of their beauty and the comforts they offer, as well as the temporary escape from the hardships of his journey home. Calypso, in particular, keeps him on her island for several years, offering him immortality and a life of ease. However, despite these temptations, Odysseus ultimately longs for his home and family, which drives him to eventually leave both women in search of his true desires. Their relationships test his resolve and highlight his complex character as both a hero and a man faced with temptation.
Odysseus refuses Calypso's offer of immortality because his ultimate goal is to return home to his wife, Penelope, and son, Telemachus. He values his mortality and his connections to his loved ones over living forever. Odysseus understands that true fulfillment comes from his relationships and the experiences he shares with those he cares about.
Odysseus quickly dismisses Calypso's offer of immortality because, despite the allure of eternal life, he yearns for the mortal experiences and connections he has left behind, particularly his longing for home and family. He values his humanity and the inevitability of death as an essential part of life's richness. Furthermore, his desire to return to Ithaca and reunite with Penelope drives him to prioritize his mortal existence over a life of isolation with Calypso. Ultimately, Odysseus's commitment to his identity and personal relationships outweighs the temptation of immortality.
Being a goddess (albeit minor) and so blessed with eternal life/youth she cannot understand why Odysseus would give up the offer of eternal youth and living with calypso in paradise in order to go back to a wife who may have forgotten him.