 Why do the Karna demand the conference begin in three days?
Every man in the Diplomatic Corps who developed a twitch or a quirk was shipped to Saarkkad IV to work under Bertrand Malloy, Permanent Terran Ambassador to His Utter Munificence, the Occeq of Saarkkad. Number two suffered from some sort of emotional block that left him continually on the horns of one dilemma or another. He was psychologically incapable of making a decision if he were faced with two or more possible alternatives of any major importance. Number three ... No two men were alike, and yet there sometimes seemed to be an eternal sameness about all men. Out there was the terrible emptiness of interstellar space—a great, yawning, infinite chasm capable of swallowing men, ships, planets, suns, and whole galaxies without filling its insatiable void. Somewhere out there, the ships of Earth were ranged against the ships of the alien Karna in the most important war that Mankind had yet fought. To have shown himself to one of them would have meant instant loss of prestige. The Occeq of Saarkkad himself was never seen except by a handful of picked nobles, who, themselves, were never seen except by their underlings. To violate the rigid social setup of Saarkkad would mean the instant closing off of the supply of biochemical products that the Saarkkadic laboratories produced from native plants and animals—products that were vitally necessary to Earth's war, and which could be duplicated nowhere else in the known universe. It was Bertrand Malloy's job to keep the production output high and to keep the materiel flowing towards Earth and her allies and outposts. A staff of top-grade men could have handled them without half trying. Not the worst ones, of course; there were places in the galaxy that were less important than Saarkkad to the war effort. "A special communication for you has been teletyped in from Earth. It had taken Malloy a long time to get it into Miss Drayson's head that it was perfectly all right—even desirable—for her to keep secrets from everyone except Malloy. She came in through the door, a rather handsome woman in her middle thirties, clutching a sheaf of papers in her right hand as though someone might at any instant snatch it from her before she could turn it over to Malloy. She wanted to know what his reaction was going to be; it didn't matter because no one would ever find out from her what he had done unless she was ordered to tell someone. "Yes, sir," said Miss Drayson in a hushed voice. Miss Drayson stood there calmly, her face a mask; her emotions were a secret.
 The Karna are skilled negotiators and want to control the peace talks.
 There is an immediate threat to the planet of Karn, and the Karna desperately need help from Earth.  The Karna are hoping to disrupt Earth's supply chain.  The Karna want to make Earth look bad in the eyes of the other planets.  The Karna are skilled negotiators and want to control the peace talks.