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.
420 blazin
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.
because he is longing for his return home to his wife and son
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.
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.
There are no details in the Odyssey that describe Calypso's physical appearance, but one might guess she was either very attractive, or could make herself appear very attractive. Her successful seduction of Odysseus, which made him forget all about his wife, stay there for years, and father their two children indicates she had more than just a sweet singing voice to offer.
Odysseus refuses the offer and he kills all of them.