Because they didn't want to be embarrassed that a man who was dressed in rags could beat them at it.
Odysseus tests the suitors by disguising himself as a beggar and observing their behavior towards him. He also sets up a challenge involving his great bow, with the condition that only someone strong enough to string the bow can marry Penelope. This test ultimately reveals the true nature of the suitors.
he make a plan and trick his mother but for a good cause penelope telemachus's mother ask the suitors to string the bow and shoot through twelve hoops but none of them could do it then the old beggar ask for a chance and the old beggar reveal his identity and kill the suitors.
Penelope set up a test for the suitors involving Odysseus' bow. She challenged them to string the bow and shoot an arrow through a row of twelve axe heads. Odysseus, disguised as a beggar, was the only one who successfully completed the challenge.
Antonous is one of the suitors trying to win over Penelope in Odysseus's absence, whom Odysseus later kills when he is in the form of a beggar, with a powerful bow at his disposal.
Antinous told the beggar that he was already lucky to have dined equally among the men, and having been allowed to listen to the suitors' conversations. Antinous accuses him of drinking too much wine.
Some were afraid that Odysseus might string the bow. Antinous accuses Odysseus of being drunk and having had too much wine. Eventually Telemachus dissipates their protests by threatening to throw stones at Eumaeus if he does not bring the bow to Odysseus; this causes the suitors to laugh heartily.
Odysseus fights the local beggar, Irus. This determines which of the beggars can stay at the table. Arnaeus was the beggar's real name, but Irus was what people called him.
Melanthius
He shot them with a bow and arrow.
-Odysseus is dressed as a beggar -He taps on his bow, as termites might have housed in his old bow. -Odysseus flung his string on the bow; it made a vibration that sounded like a hum to a swallow's song. -He was sitting on a stool while doing this. -Everyone around Odysseus, while he was standing in glory with the bow, was jealous and in awe.
The Beggar
Antinous told the beggar that he was already lucky to have dined equally among the men, and having been allowed to listen to the suitors' conversations. Antinous accuses him of drinking too much wine.