Odysseus' success in taking his suitors by surprise is that he is able to kill them because none of the suitors were expecting him to be able to string and then shoot the bow as they expected him to fail.
The purpose of the speech by Odysseus' is to announce his revenge and then let them fear what is to come.
Eurymachus responds to Odysseus because he was trying to convince him that it was really Antinous' fault that they did all the bad things so that he will be able to spare them.
The people wanted peace (out of the war in Vietnam fueled by the policy of containment) so the ones who were running for president needed to address this.
