Origins
The verb "demolish" entered English in the 1560s from French "demoliss-," the extended stem of "demolir" (to tear down, to destroy), from Latin "demoliri." The Latin word is a transparent compound of "de-" (down) and "moliri" (to build, to construct, to set in motion), which itself derives from "moles" (a mass, a massive structure, a dam, a pier). To demolish something is, at its etymological core, to un-build it — to reverse the act of construction by tearing the massive structure back down to nothing.
The Latin noun "moles" is a word of considerable interest in its own right. It denoted any large, heavy mass or structure: a dam, a breakwater, a massive building, or the effort required to move or construct such things. From this concrete sense of physical mass, "moles" developed abstract meanings related to difficulty and burden — a "moles" of trouble was a weighty mass of problems. The word gave rise to an impressive family of English derivatives: "molecule" (a small mass, coined in the seventeenth century as a diminutive), "mole" (a massive harbor breakwater), "molest" (to trouble, originally to burden with a heavy mass of difficulty), and "demolish" itself.
The verb "moliri" extended the concept of mass into action: to move masses, to build with heavy materials, to undertake laborious construction. It could also mean to set in motion more abstractly — to contrive or to attempt. This breadth of meaning is typical of Latin verbs derived from concrete nouns; the physical act of heaving stone into place became a metaphor for any effortful undertaking.
Latin Roots
When French borrowed "demolir" from Latin, the word settled into the specific sense of tearing down buildings and fortifications — a common activity in medieval warfare, where sieges frequently ended with the systematic destruction of walls and towers. English adopted the term during the sixteenth century, a period of intense military activity and equally intense borrowing from French and Latin for technical military vocabulary.
The morphological path from "demolir" to "demolish" follows the same pattern as "abolish," "astonish," "furnish," and dozens of other English verbs. French "-ir" verbs were borrowed through their present-participle stem ("-iss-"), which English adapted as "-ish." This suffix became so characteristic of French-derived verbs in English that it was sometimes added to words that did not originally possess it, as happened with "astonish."
The semantic range of "demolish" in English has always been broader than the purely architectural. From its earliest uses, the word could mean to destroy an argument, a reputation, a theory, or any abstract structure as thoroughly as one might tear down a building. This figurative extension is natural and appears in most European languages that borrowed the word. One can demolish a plate of food (consume it entirely, as if tearing it apart), demolish an opponent in debate (destroy their position utterly), or demolish a long-held belief (dismantle it piece by piece).