'anthypophoretic' originates from Greek via New/Modern Latin, specifically the Greek noun 'anthypophora' (ἀντυποφορία / anthypophorā), where elements include a form related to 'anti-/anthy-' (sense of 'in return' or 'in answer') and 'phora' from 'pherein' meaning 'to carry' (used in formation of rhetorical terms).

'anthypophoretic' changed from the New/Modern Latin rhetorical noun 'anthypophora' and the adjective-forming suffix '-etic' was attached in English to yield the adjective 'anthypophoretic'. The path is Greek → New/Modern Latin (rhetorical usage) → English adjective formation.

Initially the root referred to the act or instance of giving a counter-answer or a replied statement; over time it evolved into the technical rhetorical sense 'pertaining to the device of asking a question and immediately answering it' and the adjective describing that style.