A strong dislike or disapproval of something, or finding something unpleasant or offensive.
From 'dis-' (not, opposite) plus 'taste' (flavor, but also figuratively preference or liking). It literally means 'bad taste' in judgment or preference.
When someone says they have a 'distaste' for something, they're actually using a sensory word to describe an emotional reaction—language is constantly mixing up our senses and feelings this way.
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