Quote 1
[The Master Horse] replied, "that I must needs be mistaken, or that I said the thing which was not;" for they have no word in their language to express lying or falsehood. "He knew it was impossible that there could be a country beyond the sea, or that a parcel of brutes could move a wooden vessel whither they pleased upon water. He was sure no Houyhnhnm alive could make such a vessel, nor would trust Yahoos to manage it." (4.3.4)
Master Horse is so shocked by Gulliver's stories of countries beyond the ocean that he actually imagines that Gulliver is lying – something that the Houyhnhnms could not previously think of. You say that the Master Horse has bit of cognitive dissonance, here, meaning he's hearing something that totally doesn't fit into his worldview. It's interesting to watch this happen to someone other than Gulliver for once.
Quote 2
For [the Master Horse] argued thus: "that the use of speech was to make us understand one another, and to receive information of facts; now, if any one said the thing which was not, these ends were defeated, because I cannot properly be said to understand him; and I am so far from receiving information, that he leaves me worse than in ignorance; for I am led to believe a thing black, when it is white, and short, when it is long." And these were all the notions he had concerning that faculty of lying, so perfectly well understood, and so universally practised, among human creatures. (4.4.1)
The reason the Master Horse thinks that lying is impossible or against reason is because the point of speech is to communicate what you think. Why else would you talk? So, the thought of talking to obscure what you think seems totally inconceivable to the Master Horse.
Quote 3
He said, "he had been very seriously considering my whole story, as far as it related both to myself and my country; that he looked upon us as a sort of animals, to whose share, by what accident he could not conjecture, some small pittance of reason had fallen, whereof we made no other use, than by its assistance, to aggravate our natural corruptions, and to acquire new ones, which nature had not given us; that we disarmed ourselves of the few abilities she had bestowed; had been very successful in multiplying our original wants, and seemed to spend our whole lives in vain endeavours to supply them by our own inventions; that, as to myself, it was manifest I had neither the strength nor agility of a common Yahoo. (4.7.4)
The Master Horse thinks that the "reason" that Gulliver says European Yahoos have is really just a new kind of vice, allowing Yahoos to cheat, lie, and steal on a grander scale. And in order to practice this fake rationality, European Yahoos have given up the few natural gifts (long nails, hair to protect us from the sun) that humans have. So, what's the point of human politics and society? Does Gulliver give any kind of credit to human civilization? Do you think the book wants us to agree with Gulliver's assessment?
Quote 4
For if," said he, "you throw among five Yahoos as much food as would be sufficient for fifty, they will, instead of eating peaceably, fall together by the ears, each single one impatient to have all to itself. [...]
My master further assured me, which I also observed myself, "that in the fields where the shining stones abound, the fiercest and most frequent battles are fought, occasioned by perpetual inroads of the neighbouring Yahoos." (4.7.6, 4.7.8)
Humans are greedy. Yes, we get it, already. But Gulliver's skewing both his and the Master Horse's examples against us by never pointing out that there have been examples of humans who have given freely of themselves. Like, what about Mother Theresa? How would you argue against Gulliver's assessment of humankind?
Quote 5
My master added, "that he was daily pressed by the Houyhnhnms of the neighbourhood to have the assembly's exhortation executed, which he could not put off much longer. He doubted it would be impossible for me to swim to another country; and therefore wished I would contrive some sort of vehicle, resembling those I had described to him, that might carry me on the sea; in which work I should have the assistance of his own servants, as well as those of his neighbours." He concluded, "that for his own part, he could have been content to keep me in his service as long as I lived; because he found I had cured myself of some bad habits and dispositions, by endeavouring, as far as my inferior nature was capable, to imitate the Houyhnhnms." (4.10.7)
Sorry to all the Houyhnhnms out there, but as human beings, we find the Master Horse fairly obnoxious. Maybe we're just not rational enough to follow his supreme genius. The Houyhnhnms think Gulliver is a threat because they are concerned that he will encourage the other Yahoos of the island to rebel. They demand that Gulliver leave the island forever, and they make the Master Horse tell him so. But the Master Horse is kind enough to tell Gulliver that, for his own part, he would be happy to keep Gulliver as a servant, because Gulliver has worked so hard to overcome his "inferior nature." Patronizing, much? We have to take at least some of the Master Horse's conclusions about people with a grain of salt, because the Houyhnhnms are so intolerant of other ways of living or seeing the world.
Quote 6
My master told me, "there were some qualities remarkable in the Yahoos, which he had not observed me to mention, or at least very slightly, in the accounts I had given of humankind." He said, "those animals, like other brutes, had their females in common; but in this they differed, that the she Yahoo would admit the males while she was pregnant; and that the hes would quarrel and fight with the females, as fiercely as with each other; both which practices were such degrees of infamous brutality, as no other sensitive creature ever arrived at. (4.7.15)
The Master Horse is grossed out by the fact that human women (a) keep having sex during pregnancy (prude!), and (b) fight fiercely with human men. He also gets in a gibe that humans, "like other brutes, had their females in common." In other words, that human women can sleep with multiple men, much as animals do. What is the tone of the Master Horse's discussion of human women? Is the Master Horse's assessment of human women consistent with other parts of Gulliver's own analyses of women? Do you get the sense that the novel of Gulliver's Travels as a whole supports a poor opinion of women, or do different sections contradict each other?