The executioner's argument was that you couldn't cut of something's head unless there was a trunk to sever it from. He'd never done anything like that in his time of life, and wasn't going to start now. The King's argument was that anything that had a head, could be beheaded, and you weren't to talk nonsense. The Queen's argument was that if something wasn't done about it in less than no time, she'd have everyone beheaded all round. It was this last argument that had everyone looking so nervous and uncomfortable.
The executioner argued that a head could only be cut off if there was a trunk to separate it from, claiming he had never attempted such an act and wouldn't start now.
The King countered by stating that anything with a head could be beheaded and dismissed the executioner's doubt as nonsense. The Queen, however, demanded immediate action, threatening to have everyone beheaded if the situation wasn't resolved quickly, causing everyone to feel tense and uneasy.