'anti-radically' originates from Modern English as a formation combining the prefix 'anti-' (from Greek 'anti', meaning 'against'), the adjective 'radical' (from Latin 'radicalis', from 'radix' meaning 'root'), and the adverbial suffix '-ly' (from Old English '-lic'/'-ly' meaning 'having the nature of' or 'in the manner of').

'anti-radically' was formed by adding the suffix '-ly' to 'anti-radical' (a compound of 'anti-' + 'radical'). 'Radical' came into English via Medieval/Modern French and Middle English from Latin 'radicalis' (ultimately from 'radix', 'root'), and 'anti-' entered English from Greek through Latin and Old French; the adverbial '-ly' is the regular Modern English adverbial ending.

The root 'radical' originally meant 'of or relating to roots' and then 'fundamental' or 'thorough.' Over time it gained the sense 'favoring thorough or extreme change.' 'Anti-radically' thus evolved to mean 'in a manner opposed to such thorough or extreme change' and is now used to describe actions or attitudes resisting radical approaches.