dislike, detest, hate
嫌 centers on a strong negative feeling toward something: disliking, detesting, or hating it.
嫌 combines 女 (woman) with 兼, which likely contributes the sound and may suggest a sense of being combined or involved, but the exact semantic link to dislike is uncertain.
A woman 女 beside 兼, which looks like a hand holding two things together. Imagine a woman forced to combine with something she hates, making her dislike it intensely.
For ケン, picture Ken, a man who strongly dislikes something, making a disgusted face: Ken -> ケン, and his dislike is clear.
disliking; not wanting; unwilling (to do); reluctant
disliked; hated; disagreeable
to hate; to dislike; to loathe; to abhor
humour; humor; temper; mood; spirits
hating; strongly disliking
harassment; pestering
disgust; hate; repugnance; loathing
unpleasant; disagreeable; nasty
to appear uncomfortable (with); to seem to hate; to express dislike
likes and dislikes; tastes; preferences; pickiness (esp. about food); choosiness; fussiness
dislike; disgust; disinclination; tired of
disagreeableness; unpleasantness; nastiness; offensiveness; tastelessness
nice to see you; good morning; good evening
suspicion
hating to lose; unyielding; unbending; competitive; sore loser; determined
antipathy; prejudice
good humour (humor); good mood
misanthropy; misanthrope
disliking a certain food without having tried it
dislike of smoking