'antilogical' originates from modern English, formed from the combining form 'anti-' (ultimately from Greek 'anti') and 'logical' (from Greek 'logikos' via Latin and Old French), where 'anti-' meant 'against' and 'logos/logikos' meant 'reason' or 'speech'.

'logical' entered English via Old French 'logique' and Latin 'logica', from Greek 'logikos' (from 'logos'). The prefix 'anti-' has been used in English from Greek 'anti' ('against'). These elements were combined in English to form 'antilogical' (a late formation reflecting 'anti-' + 'logical').

Initially the components meant 'against' + 'reason'; the combined form has consistently meant 'against logic' or 'contrary to reason' and has retained that core meaning.