When a thought, a plan, or a story does not follow from the facts or from good reasons, we can name that failure. Illogicality is that name: the way something fails to hang together, or one place where the thinking jumps. You will see it more in essays and reviews than in speech. In class or on the street, people usually say “that doesn’t make sense” or call the thing illogical. Though actually you can point to more than one (several illogicalities in the plot), many writers treat it as one mass: the illogicality of the argument.