'anti-' originates from Greek, specifically the word 'antí', where 'anti-' meant 'against'; 'argumentative' originates from Latin via Old French, from 'argumentum' (Latin) meaning 'a proof or discussion', with the adjectival suffix '-ative'.

'argument' came into English from Old French and Latin ('argumentum'), and the adjective 'argumentative' developed in English by adding '-ative' to 'argument'; the prefix 'anti-' (Greek) has been used productively in modern English to form compounds such as 'anti-argumentative' to mean 'against argument' or 'opposed to arguing'.

Initially the roots meant 'against' (for 'anti-') and 'a reason, proof, or discussion' (for 'argumentum'); combined in modern formation the compound has come to mean 'opposed to arguing' or 'not inclined to argue'.