Answer:
They are worried about their reputations.
Explanation:
After losing all his companions, Ulysses managed to get to Ithaca. He was old and tired and disguised as a beggar not to be recognized.
Odysseus in the presence of Penelope, without being recognized, confided that her husband was alive and tried to return to Ithaca. Penelope revealed to him that she could not stand the pressure of having to marry, and that the next day she would run a contest to choose one of her suitors as her husband. It would be a winner who could shoot an arrow with the bow of Odysseus, who was to cross the hole of twelve axes lined up on the ground.
The next day, none of the suitors got the arrow. It was when the "beggar" under the laughter of disapproval of the suitors asked to be allowed to participate in the race.
Odysseus, authoritatively and effortlessly, threw the right arrow toward the axes. Then, with Telemachus and his faithful servants, he killed all the suitors and the traitorous employees, assuming his true identity.