嫌がる
いやがる · iyagaru · JLPT N2 · verb-godan
to dislike
嫌 iya (ugh, no!) + がる (to act like it) = to show you don't want it
いや is the everyday Japanese cry of 'no!' or 'ugh'. Adding がる turns a feeling into visible behaviour, as in 寒がる (to act cold). So 嫌がる means showing reluctance, usually said about someone else.
嫌 — woman radical 女 + 兼 (combine, phonetic)
A semantic-phonetic compound: 女 (woman) suggests the meaning, while 兼 supplies the sound. The original sense related to suspicion or dislike, possibly tied to social judgments. Over time it broadened to mean 'to dislike,' 'to suspect,' or 'to find objectionable.'