Origins
A rebel does not merely fight — a rebel fights back. The word comes from Latin rebellis, meaning 'making war again', composed of re- ('again, back') and bellum ('war'). In Roman usage, rebellāre described the most dangerous kind of enemy: a conquered people who refused to stay conquered.
The re- prefix carries the entire weight of the word. An ordinary enemy wages bellum. A rebel wages it twice — after defeat, after submission, after the matter was supposed to be settled. Rome's wars against Gallic and Germanic rebels were wars against people who had already surrendered.
Latin Roots
The Latin bellum produced a rich family of English words. Belligerent means 'war-waging'. Bellicose means 'war-inclined'. Antebellum means 'before the war'. Even the word duel has a connection: it descends from duellum, an archaic form of bellum.
The word reached English through Old French during the 14th century, an era of revolts — the Jacquerie in France, the Peasants' Revolt in England. The timing was not accidental. When people needed a word for armed resistance against authority, Latin had one ready.