'anti-anarchist' originates from Modern English, formed by the prefix 'anti-' (from Greek 'anti' meaning 'against') combined with 'anarchist' (from French/English 'anarchist').

'anarchist' derives from Greek 'anarkhos' ('an-' meaning 'without' + 'arkhos' meaning 'ruler'), passed into Late Latin and French as 'anarchiste' and then into English as 'anarchist'; the prefix 'anti-' comes from Greek 'anti-' and has been used in English since Classical/Medieval times to form oppositional compounds, resulting in the compound 'anti-anarchist' in Modern English.

Initially the elements meant 'against' + 'one without a ruler'; combined as 'anti-anarchist' the term has meant 'opposed to anarchism' since its formation and has retained that basic meaning.