'anti-elitistically' is formed in modern English by combining the prefix 'anti-' (from Greek 'anti-' meaning 'against') with 'elitistic' (derived from 'elite' + '-istic') and the adverbial suffix '-ally'.

'elite' entered English from French 'élite', which came from Latin roots related to 'eligere' ('to choose'); 'anti-' is a Greek prefix meaning 'against'. The adjective 'elitistic' and related forms (e.g., 'elitist') developed in English; the adverbial formation 'anti-elitistically' is a modern derivation formed by adding '-ally' to the adjective.

Originally the elements meant 'against' (anti-) and 'chosen' or 'selected' (elite from Latin 'eligere'); over time the combined modern form has come to mean 'in a manner opposed to elites or elitism.'