because she was lonely and she likes him
Calypso offers immortality to Odysseus
Hermes tells Calypso to let Odysseus go.
Odysseus met Calypso on her lush island of Ogygia.
Calypso
Calypso has the power of immorality over Odysseus.
Hermes is sent down to Calypso, telling her that the gods wish for her to release Odysseus. Therefore, it is Calypso who allows Odysseus to leave, not Odysseus who 'manages to say no.'
Calypso detains Odysseus because she has fallen in love with him and desires to keep him on her island, Ogygia, as her companion. She offers him immortality and eternal youth, hoping to persuade him to forget his longing for home and family. Despite her affection, Odysseus yearns to return to Ithaca and his wife, Penelope, which ultimately leads to his rescue by the gods, particularly Hermes, who commands Calypso to let him go.
Calypso and Odysseus become lovers. Calypso offers Odysseus immortality and eternal youth if he would stay with her. Calypso does not aid Odysseus' escape until told to do so, so he seemed trapped on her island without a ship.
Calypso
Calypso wants Odysseus to stay with her on the island forever.
No! Poseidon tries to drown Odysseus during his escape from Calypso. Athena and Hermes assist Odysseus.
Calypso