How does Gulliver's voyage to the land of Houyhnhnms constitute the height of Swift's irony in Gulliver's Travels?
The voyage to the land of the Houyhnhnms shows the ultimate destination of the unfortunate Gulliver; through each prior voyage he has held steadfast to the morality and dignity of his homeland and his countrymen, although his ideals were challenged many times. However, when confronted with what seems a perfect Utopian society, one in which humans are animals and horses are intelligent and civilized, Gulliver's alliance breaks down at last. He cannot argue with the rational arguments of the Houyhnhnms and becomes a self-loathing Yahoo.
...I entered on a firm resolution never to return to humankind... in what I said of my countrymen, I extenuated their faults as much as I durst before so strict an examiner; and upon every article gave as favourable a turn as the matter would bear. For, indeed, who is there alive that will not be swayed by his bias and partiality to the place of his birth?
(Swift, Gulliver's Travels, gutenberg.org)
The irony comes when Gulliver accepts that he is most at home in an inhuman society; on his return to England he can barely be in the same room with other humans. Throughout his travels, he always found the means and the need to return to his home life and land, both physically and mentally; at the end of the book, he is safely home, but trapped among creatures he abhors. Gulliver has completed his journeys and found the reason and purpose he sought, but at the cost of his link to human society.