Odysseus chooses to leave immortality and the splendid life offered by Calypso in exchange for a dangerous sea voyage because he is homesick and wants to return home to his wife, Penelope.

That being the case, he looks upon Calypso's offer of his becoming her immortal husband as a kind of imprisonment. Odysseus knows that if he accepts Calypso's offer, he will never be able to return to Ithaca, which is what he wants more than anything else in the world.

Odysseus has been away from his home for twenty years and is understandably keen to get back there as soon as possible. Already heartsick from his extended stay on Calypso's island of Ogygia, Odysseus isn't going to feel any better if he stays there forever as an immortal.

For the last seven years, he's effectively been Calypso's prisoner. But as he's mortal, he still has the chance to escape and return to Ithaca. Such an opportunity would be gone forever if Odysseus took up Calypso's offer of marriage and became an immortal.