"Rebellion" is the conversation in which Ivan tells Alyosha, in the tavern, why he does not accept God's world: because no future harmony is worth the tears of a single child who suffered without guilt.
Ivan starts with love of one's neighbor, which he finds impossible up close, and then chooses children, because they have not yet eaten the apple and cannot pay for any sin. He cites cases he says he has collected: the Turks in Bulgaria, the five-year-old girl locked in the cold by educated parents, who beats her breast and prays to "dear little God," the general who sets his dogs on an eight-year-old boy in front of the boy's mother. He asks Alyosha what should be done with the general. Alyosha answers: shoot him.
The conclusion has two images. The mother has no right to forgive her son's executioner, and Ivan does not want the embrace that the final harmony promises. And the ticket: he does not reject God, he only returns, with the greatest respect, his ticket of admission. Alyosha calls it rebellion, and Ivan finds the word strange: can one live on rebellion? He wants to live.
Before telling the poem of the Inquisitor, Ivan asks the architect's question: would Alyosha agree to build the peace of mankind on the suffering of a single child? Alyosha says no. And he answers that there is a being who can forgive, because he gave his own innocent blood. It is the only reply that rebellion receives, and Ivan was expecting it.