In a manner that shows or expresses strong natural dislike or opposition.
Adverbial form of antipathetical, adding -ly to the adjective. This stacking of suffixes (anti- + path- + -etical + -ly) is typical of how English builds increasingly specific descriptive terms through layering.
English loves these adverb forms that add -ly to already complex adjectives, creating tongue-twisting words that sound impressive but mean simply 'in an opposed way.' You'll rarely hear this spoken aloud—it's almost exclusively a written, formal word.
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