'antigrammatical' originates from Greek and Late Latin elements: specifically the prefix 'anti-' from Greek 'anti' where 'anti-' meant 'against', and 'grammatical' via Late Latin 'grammaticalis' ultimately from Greek 'gramma' meaning 'letter'.

'antigrammatical' was formed in modern English by combining the Greek-derived prefix 'anti-' with the adjective 'grammatical' (which came into English through Latin and Old French from Greek 'gramma').

Initially it literally meant 'against grammar' and over time has come to be used to describe expressions or constructions that violate or are not acceptable under standard grammatical rules ('not grammatical').