'arch-critic' is a compound of the prefix 'arch-' and the noun 'critic'. 'arch-' originates from Greek, specifically the word 'arkhós' (often represented as 'arkh-'), where 'arkh-' meant 'chief, principal'. 'critic' originates from Greek, specifically the word 'kritikos', where 'krit-' meant 'able to judge'.

'arch-' passed into English usage via Latin/Old French forms and was used as a combining form in Middle and Modern English; 'kritikos' became Latin 'criticus' and Old French 'critique', then Middle English 'critic', and the compound 'arch-critic' arose in modern English by combining the prefix and noun.

Initially, 'arch-' meant 'chief' or 'principal' and 'critic' meant 'judge' or 'one who discerns'; over time 'arch-' also developed an intensifying sense ('extreme' or 'notorious'), while 'critic' specialized to mean a reviewer or someone who expresses disapproval. Thus 'arch-critic' can mean either the chief critic or an especially severe critic.