'rout' originates from Anglo-French/Old French words like 'route' or 'rout', used to denote a flight, stampede, or disorderly crowd; the word likely reflects Germanic/Frankish influences meaning a rush or breaking up of a group.

'rout' appeared in Middle English (e.g. Middle English 'routen'/'rout') meaning a disorderly flight or tumult; it continued into Modern English with senses of both a chaotic dispersal and, by extension, a crushing defeat.

Initially, it meant a noisy disturbance or a disorderly flight; over time one of its main modern meanings became 'a decisive defeat' (i.e., the defeated party's flight), while the older sense of a noisy gathering became archaic.