This is not an idiom at all.
"abhorrent" means "detestable" o "repugnante" o "aborrecible."
E.g. the idea is abhorrent to me : la idea me resulta repugnante
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If we take away the adjectives and relative clause, the sentence would read "All emotions were abhorrent to his mind." 'Cold, precise but admirably balanced' are all describing his 'mind.'





