For the cheesiest reason possible: he loves only his wife, he misses her, and wants to go home.
I would think that would be obvious as that's the reasoning he gives Circe.
he said that he didnt want to be seen with her for fear that her father would get mad
Cdyfyf
She clearly says (book 6) she is afraid of the gossip if she comes home with a strange man.
Odysseus wishes to return home to see his wife Penelope and his child Telemachus, whom he has not seen for 20 years.
Because then his men wouldn't want to leave.
Calypso allows Odysseus to leave her island after Athene asks Zeus to tell Calyspo that if she doesnt allow Odysseus to leave her island that if she doesnt that Zeus will strike her with a thunderbolt and kill her as he is not a prisoner to her island and need to get home to be with Penelope (his wife). Zeus sends Hermes the messenger God to tell Calypso. Although Calypso is furious and doesnt want Odysseus to leave, she lets him because obviously she doesnt want to die so she helps him build a raft and gives him gifts for his journey home.
He didnt want to scare them so they wouldn't leave.
Irus, a beggar in Homer's "Odyssey," challenges Odysseus to a fight when Odysseus, disguised as a beggar, arrives at the palace of Odysseus. Irus wants to assert his dominance and maintain his status among the other beggars by defeating Odysseus. However, he underestimates Odysseus, who ultimately showcases his strength and skill by defeating Irus in the contest. This confrontation serves to highlight Odysseus's resilience and capabilities even in disguise.
Odysseus wants to leave Calypso and her island because he wants to go home to Ithaca. After the Trojan war, his ship was tossed off course and he has been trying to finish his journey since.
Antinous and the other suitors are confident they can stay in Odysseus' palace because they believe Odysseus is dead, and they view themselves as the rightful claimants to his wealth and position. They exploit the absence of Odysseus, assuming they can take over his household without consequence. Their arrogance is fueled by the support of powerful families and their own social status, leading them to underestimate the possibility of Odysseus's return. This sense of entitlement blinds them to the impending doom they face.
they have a good time, and odysseus doesn't want to leave, but they make him, the gods said no more of this madness
Odysseus way loyal to his men, he didn't want to leave any behind ie: lotus, sirens, ect... Penelope stayed loyal to Odysseus even thought he was gone for such a long time