Antinous seems to have an air of self-importance, and believes he is far better than a beggar. For a beggar to even talk to him is considered an insult to him.
Chat with our AI personalities
The suitors believe Odysseus to have killed Antinous by mistake, and they threaten to kill him as well.
Antinous has always been rich. He is incredibly arrogant, and thinks that his social stature makes him better than others. Antinous looks down upon the poor as if they have some sort of contagious disease. Any attacks on his standing or character are taken poorly. When Odysseus, the beggar, criticizes him, Antinous does not take it well. It is possible that he may be compensating for his inadequacies in other areas such as fighting.
The other suitors do not think it right that Antinous has assaulted Odysseus (the beggar), and warn that it may be some god in disguise. After realizing that Odysseus has killed Antinous intentionally and intends to kill them all, they try to appease Odysseus by blaming all the trouble on Antinous.
The suitors react with outrage, and threaten to kill Odysseus. They think the killing is an accident and still do not realize Odysseus' identity or intentions.
Antinous' and Eurymachus' reaction to the challenge is they think it is unreasonable and it is not possiable. "Not a shred of sense in your head, you filthy drifter"