'antistrophic' originates from Greek, specifically the word 'antistrophikos', where 'anti-' meant 'against' and 'strophe' meant 'a turning or verse'.

'antistrophikos' passed into Late Latin/Medieval usage (seen in forms like 'antistrophicus') and via later scholarly or French formations (e.g. 'antistrophique') the adjective entered English as 'antistrophic'.

Initially it meant 'pertaining to or acting as an antistrophe (a responding or counter turn)'; over time this basic sense has been retained, now describing something that alternates with or corresponds to another section.