'antiorthodoxly' originates from Modern English, specifically the elements 'anti-' + 'orthodox' + the adverbial suffix '-ly', where 'anti-' meant 'against', 'orthodox' came from Greek 'orthodoxos' meaning 'correct belief', and '-ly' forms adverbs.

'orthodox' comes from Greek 'orthodoxos' (orthos 'straight/correct' + doxa 'opinion/glory'), passed into Late Latin and Old French before becoming Middle English 'orthodox' and modern English 'orthodox'; the prefix 'anti-' (from Greek 'anti-' meaning 'against') was attached in Modern English to form 'antiorthodox', and '-ly' was added to create the adverb 'antiorthodoxly'.

Initially, 'orthodox' meant 'holding correct belief', but with the addition of 'anti-' the compounded form meant 'opposed to orthodox belief'; the adverb 'antiorthodoxly' specifically expresses doing something in a manner opposed to established doctrines or the Orthodox institution.