In Edwardian era London, Gabriel Syme is recruited at Scotland Yard to a secret anti-anarchist police corps. Lucian Gregory, an anarchistic poet, lives in the suburb of Saffron Park. Syme meets him at a party and they debate the meaning of poetry. Gregory argues that revolt is the basis of poetry. Syme demurs, insisting the essence of poetry is not revolution but law. He antagonises Gregory by asserting that the most poetical of human creations is the timetable for the London Underground. He suggests Gregory isn't really serious about anarchism, which so irritates Gregory that he takes Syme to an underground anarchist meeting place, revealing his public endorsement of anarchy is a ruse to make him seem harmless, when in fact he is an influential member of the local chapter of the European anarchist council.
The central council consists of seven men, each using the name of a day of the week as a cover name; the position of Thursday is about to be elected by Gregory's local chapter. Gregory expects to win the election but just before, Syme reveals to Gregory after an oath of secrecy, that he is a secret policeman. Fearful Syme may use his speech in evidence of a prosecution, Gregory's weakened words fail to convince the local chapter that he is sufficiently dangerous for the job. Syme makes a rousing anarchist speech and wins the vote. He is sent immediately as the chapter's delegate to the central council.
In his efforts to thwart the council, Syme eventually discovers that the other five members are also undercover detectives; each was employed just as mysteriously and assigned to defeat the Council. They soon find out they were fighting each other and not real anarchists; such was the mastermind plan of their president, Sunday. In a surreal conclusion, Sunday is unmasked as only seeming to be terrible; in fact, he is a force of good like the detectives. Sunday is unable to give an answer to the question of why he caused so much trouble and pain for the detectives. Gregory, the only real anarchist, seems to challenge the good council. His accusation is that they, as rulers, have never suffered like Gregory and their other subjects and so their power is illegitimate. Syme refutes the accusation immediately, because of the terrors inflicted by Sunday on the rest of the council.
The dream ends when Sunday is asked if he has ever suffered. His last words, "can ye drink of the cup that I drink of?", is the question Jesus asks St. James and St. John in the Gospel of Mark, chapter 10, vs 38â39, to challenge their commitment in becoming his disciples.

Question: Why does Gregory challenge the central council?
Answer: because he believes they have never really suffered
Alternative answer: They had never suffered, making them illegitimate.