The shortest chapter in Part I and its closing argument. The Underground Man turns the crystal palace image directly on the reader: you believe in a palace of crystal that can never be destroyed, one at which you will not be able to put out your tongue or make a long nose even on the sly. And perhaps THAT is just why he fears it. Not because it is perfect, because it is indestructible. Because even small, private defiance is impossible inside it.
The hen-house: if it were merely a hen-house rather than a palace, he might creep into it to avoid getting wet, but he would not call it a palace out of gratitude for keeping him dry. You say a hen-house is as good as a mansion. He answers: yes, if one had to live simply to keep out of the rain. But what if he has taken it into his head that this is not the only object in life? What if, if one must live, one had better live in a mansion? That is his choice. His desire. The only way to eradicate it is to change his preference, give him another ideal, allure him with something better. Until then, he will not take the hen-house for a mansion.
The crystal palace may be an idle dream, inconsistent with the laws of nature, invented through his own stupidity. He does not dispute this. What does it matter? It exists in his desires. He will put up with any mockery rather than pretend to be satisfied when hungry. What he will not accept as the crown of his desires: "a block of buildings with tenements for the poor on a lease of a thousand years, and perhaps with a sign-board of a dentist hanging out." Destroy his desires, show him something better, and he'll follow. Otherwise he can retreat to his underground hole. While alive and possessing desires: he would rather his hand were withered off than bring one brick to such a building.
Then the clarification, because it will be misread. He did not reject the crystal palace simply because one cannot stick one's tongue out at it. He is not particularly fond of sticking his tongue out. What he resented was that of all the edifices ever constructed, there has not been a single one at which one COULD NOT put out one's tongue. He would let his tongue be cut off out of gratitude if things could be arranged so that he lost all desire to put it out. It is not his fault things cannot be arranged that way.
The chapter, and all of Part I, closes on a question and a self-deprecating admission. The question: "Can I have been constructed simply in order to come to the conclusion that all my construction is a cheat? Can this be my whole purpose? I do not believe it." The admission: underground folk ought to be kept on a curb. They may sit forty years in silence underground, but when they come out into the light and break out, they talk and talk and talk.
