This is more of a historical-rhetorical observation than succinct answer, already provided by "Laws of Thought" reply.
Let's ask first, what is an irrational explanation? Not merely illogical or nonsensical. It may be purely emotive. "Because we MUST!" It may take the form of a "because" and refer to a "cause" that is not falsifiable. "Because I want it." It may even take the form of a chant. "USA! USA! USA!" Perhaps the most common form, which combines all these is the appeal to authority. "Because... everyone does it, Aristotle proved it, God commands it, it was always thus, etc.
According to the work of Walter Ong, Eric Havelock, and other classicists, this was the common form of knowledge transmission in oral society, specifically, the Homeric tradition. Values, codes, and knowledge had to be "memorized" in poetic form, commands,rhymes, and "sayings," because that was the only way to store culture and pass it on. Much like our first interlocutions with children.
The prerequisite of "reasoning," then, is writing. The shift from oral, Homeric culture to the Greek's unique phonetic alphabet turned words into preserved, visual objects, no longer actions and events in flux. Court oratory, proclamations, drama, histories, dialectic could all be "written down" like pinned specimens, preserved, examined, debated.
This "visualizing" of speech came alongside the visual demonstrations of geometry, where "reasoning" from common axioms was carried out visually with line and compass to "show" what follows from coherent "ratios." Similar "lines" of proportional reasoning could be followed in the developing "logoi" of written arguments. (See Plato's Phaedrus for contemporary thoughts on the matter.)
This, anyway, is Havelock's thesis pertaining to the cultural trauma of alphabetized speech and the origins of Plato's "rational" attacks on the poets and Homeric tradition, with their appeals to heroism, authority, tradition, and other forms of "irrational" persuasion. I, for one, find it quite compelling and illuminating.
So, "rational" explanations are a type of rhetoric and persuasion. They appeal to commonly accepted axioms and a coherent development of "ratios" and symmetries, not unlike geometrical theorems. They may retain, but supersede, oral appeals to memorization, rhyme, emotion, authority. They may be deductive or inductive, factual or not. But they must cohere proportionally within an implied whole, such as "the universe," as in a visual demonstration of the Pythagorean theorem outlined in the sand.