The source of the word is Plato's dramatic work Phaedo (Φαίδων in Attic Greek), which presents the final hours and execution of Socrates, ultimately, by those who were offended by his philosophical pursuit.
Plato’s Phaedo tells the story of Phaedo of Elis recalling the death and final hours of Socrates some time afterwards to Echecrates, who had heard tell of Socrates' execution but has no detailed account and is curious to hear of it. Phaedo, being one of those present at Socrates' execution, begins and explains that he and others had gathered early to visit Socrates on the day of his execution. There, Simmias and Cebes had begun a discussion with Socrates on the afterlife, and Cebes in particular had questioned Socrates on his belief that the soul must be immortal. Phaedo recalls that Socrates had just presented an argument to this effect, when both Simmias and Cebes presented excellent objections. Phaedo breaks from his story and says to Echecrates:
When we heard what they [Simmias and Cebes] said we were all depressed, as we told each other afterwards. We had been quite convinced by the previous argument [Socrates' argument], and they seemed to confuse us again, and to drive us to doubt not only what had already been said but also what was going to be said, lest we be worthless as critics or the subject itself [the fate of the soul] admitted of no certainty.—Plato, Phaedo, 88c 
Phaedo then tells Echecrates that before replying to Simmias and Cebes' argument Socrates, having no doubt seen the disquiet that their objection had caused among all those present, which Phaedo himself evidenced above to Echecrates, breaks from his argumentation to make an important point: that they must not lose heart because of this objection and reject philosophy as a result. Phaedo says that Socrates begins thus:
...but first there is a certain experience we must be careful to avoid...That we must not become misologues, as people become misanthropes. There is no greater evil one can suffer than to hate reasonable discourse. Misology and misanthropy arise in the same way. Misanthropy comes when a man without knowledge or skill has placed great trust in someone and believes him to be altogether truthful, sound and trustworthy; then, a short time afterwards he finds him to be wicked and unreliable, and then this happens in another case; when one has frequently had that experience, especially with those whom one believed to be one's closest friends, then, in the end, after many blows, one comes to hate all men and to believe that no one is sound in any way at all...This is a shameful state of affairs...and obviously due to an attempt to have human relations without any skill in human affairs.—Plato, Phaedo, 89d–e 
Plato's Socrates is warning the reader that, just as one should not hate his fellow man because they themselves were poor in judging character, they should not hate argumentation and reason — partake in "misology" — just because they may not be skilled enough to discern the flaws and strengths of an argument:
It would be pitiable...he [Socrates] said, when there is a true and reliable argument and one that can be understood, if a man who has dealt with such arguments as appear at one time true, at another time untrue [just as Socrates' argument had appeared to those present], should not blame himself or his own lack of skill but, because of his distress, in the end gladly shift the blame away from himself to the arguments, and spend the rest of his life hating and reviling reasonable discussion and so be deprived of truth and knowledge of reality...This then is the first thing we should guard against, he [Socrates] said. We should not allow into our minds the conviction that argumentation has nothing sound about it; much rather we should believe that it is we who are not yet sound and that we must take courage and be eager to attain soundness.—Plato, Phaedo, 90c–e 
The word misology itself is first attested in English in 1833, and was used in Benjamin Jowett's 1871 translation of Plato's work, Dialogues: "as there are misanthropists or haters of men, there are also misologists or haters of ideas."
The term was also used by Immanuel Kant in a passage from his 1785 work, Groundwork of the Metaphysics of Morals (Grundlegung zur Metaphysik der Sitten): "Misologie, d. i. [das ist] haß der vernunft" translated by Thomas Kingsmill Abbott in 1895, straightforwardly, as: "misology, that is, hatred of reason."
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