The word 'unteachable' is a modern English formation built upon the core Germanic verb 'teach.' The concept of teaching itself originates from the Proto-Germanic taikijaną, meaning "to show" or "to point out," a sense still preserved in its connection to the word 'token.' The suffix '-able,' entering English via French from the Latin '-abilis,' attaches to verbs to create adjectives meaning "capable of undergoing the action." Finally, the Old English negative prefix 'un-' is applied to invert the meaning. Thus, the literal morphemic construction "not capable of being taught" evolved directly into its modern abstract senses, describing either an intractable pupil or an inherently inexplicable subject.

Structure: un (not) + teach (instruct) + able (capable of) - un: A prefix of Germanic origin (Old English un-), meaning "not." It functions as a negative particle. - teach: A verb of Germanic origin (Old English tǣcan), meaning "to show, instruct, or point out." It functions as the core lexical root. - able: A suffix of Latin origin (via Old French -able), meaning "capable of, fit for, or worthy of." It functions as an adjective-forming suffix.