Odysseus wanted to leave Kalypso and her island because he missed his wife, his son and his homeland. He stayed on Kalypso's island for 7 years.
In Homer's "Odyssey." Odysseus was the son of King Laertes of Ithaca. After winning the Trojan War, Odysseus and his men were on their way home in victory. However, Poseidon, god of the sea, shipwrecked Odysseus and drowned his men. Odysseus landed on Ogygia, which was Kalypso's island.
When she found Odysseus, Kalypso fell in love with him. He stayed with her for 7 years, and although he had two sons with Kalypso and she tried to bribe him with immortality, Odysseus wanted to return home to his family. Athena rescued Odysseus from Ogygia by having Zeus send Hermes with the message that he should return home. Kalypso helped him build a raft and let him leave for Ithaca.