'non-anselmic' originates from English, specifically the prefix 'non-' and the name 'Anselm', where 'non-' meant 'not' and 'Anselm' comes from the Old Germanic personal name 'Anselm' (later Latinized 'Anselmus').

'Anselm' comes from Old High German 'Anselm' → Latinized 'Anselmus' in medieval Latin → used in reference to Saint Anselm and his ideas, producing the adjective 'Anselmic' and, by prefixation, 'non-anselmic'.

Initially 'Anselm' was a personal name; over time 'Anselmic' came to mean 'relating to Anselm's ideas', and 'non-anselmic' came to mean 'not relating to or not supportive of those ideas'.