What does the king of Brobdingnag discuss with Gulliver?

This is one of the most incisive and sharply satiric portions of Swift's work—and one of the most hilarious. It's clear from this point (if not before) that Gulliver is a foil for Swift's own views and that Gulliver is setting himself up for a dose of reality at the hands of the Brobdingnagian king. Gulliver, like most Englishmen of his time, sees his own country as a model of advancement and the height of civilization. It is not just the English, but the European mindset of the time that Gulliver is expressing in boasting of the achievements of his people and their legal system. Yet when he's completed his descriptions, not only is the king unimpressed, but he draws the conclusion that the English are "the most pernicious race of odious vermin that nature ever suffered to crawl upon the surface of the earth." To some extent, the mythical lands Gulliver visits in his travels are symbolic of the actual outside, non-European world which was in the process of being colonized by the European powers. The assumption of the English, French, Spanish, and Portuguese was, of course, that the "natives" of non-European cultures needed to have civilization and Christianity brought to them in order to "improve" their lives and to "save their souls." The Brobdingnagian king's comments are intended by Swift as a debunking of the arrogance and superiority of the English and the other Christian nations—just as the entire book is a satire on mankind's pretensions and follies as a whole.

The king of Brobdingnag discusses England, Gulliver's home, with Gulliver at great length.  Gulliver delights in telling him about the British government, about British courts and laws, and even British weaponry.  The Brobdingnagian king, however, is utterly horrified to learn of the behavior of individuals in the government, the way people seem to abuse the courts, the way people lie and cheat, and so forth.  He is most disgusted to learn of gunpowder, though.  When Gulliver explains the effects of gunpowder and offers to tell the king the recipe, the king rebuffs him in no uncertain terms.  He calls Gulliver and his entire species odious vermin who really do not deserve to live at all.  As a peace-loving king who sees his office as a duty to protect the citizens of Brobdingnag, the king of Brobdingnag wants nothing to do with the ways and customs of England or humanity.