In Gulliver's Travels, what does Gulliver believe to be true about the Houyhnhnms?
Through his interactions with the Houyhnhnms, Gulliver decides that their society, which is entirely peaceful and with almost no concept of falsehoods, must be the ideal and perfect society which Humankind has sought for centuries. Humankind used war to try and create their own Utopias, but the Houyhnhnms use rationality and pure logic to create a society without war or conflict. Gulliver notes that there is no crime of any sort, and no reasons for any conflict. Houyhnhnm culture is comparable to the Biblical Garden of Eden, where there is no conflict or strife, but also no passion or creative desire. Gulliver finds it almost unthinkable that Yahoos -- even "civilized" Yahoos such as himself -- could ever rise to the example set by the Houyhnhnms.
...how could I think with temper of passing my days among Yahoos, and relapsing into my old corruptions, for want of examples to lead and keep me within the paths of virtue? that I knew too well upon what solid reasons all the determinations of the wise Houyhnhnms were founded, not to be shaken by arguments of mine, a miserable Yahoo.
(Swift, Gulliver's Travels, eNotes eText)
This reasoning leads Gulliver to shun other humans, since he believes that he has found the perfect society in the Houyhnhnms and cannot hope to be happy among people he views as Yahoos. His belief is founded both in his treatment by the Houyhnhnms, who at first accept his ability to reason, and by his observations of the Yahoos, with whom he increasingly finds parallels in Humankind. In the end, he believes that Humans might someday be able to supercede their baser, Yahoo-like natures, and become more like the Houyhnhnms, who he admires for their peaceful nature and stable society.
Gulliver sympathizes with and prefers the Houyhnhnms to the Yahoos, even though the Yahoos seem more ethnically similar to Gulliver. Of the civilizations he visits, he identifies most with the Houyhnhnms. Their entire civilization is based on nothing but cold, hard, logical reason, which means they do not follow a religion and they practice eugenics. One might look at this chapter a little more closely: how could Swift be arguing for the death of the "unworthy"? Would he argue for that? Take a look at A Modest Proposal, linked below, and remember that Swift is notoriously satirical, sarcastic, and a hilarious genius. Perhaps, just perhaps, Gulliver is a victim of Swift's pen.