1Disliked, hated, or found unpleasant -- expresses aversion or a lack of liking (na-adjective / noun).
私は納豆が嫌いです。
I dislike natto.
彼の態度がどうしても嫌いだ。
I really dislike his attitude.
嫌いなら無理に食べなくていいよ。
If you don't like it, you don't have to force yourself to eat it.
好き嫌いが多くて、給食の時間が苦手だ。
I have a lot of likes and dislikes, so I don't enjoy school lunch time.
2A tendency or propensity, used in the set phrase "~の嫌いがある" ("tends to ~"); a somewhat formal equivalent of "~しがち".
彼は忘れっぽい嫌いがあるから注意が必要だ。
He tends to be forgetful, so you need to be careful.
その提案は短絡的な嫌いがある。
That proposal tends to be overly simplistic.
3A more literary, somewhat old-fashioned usage meaning "distinction" or "discrimination"; most often seen in the pattern "~の嫌いなく" ("regardless of ~").
この賞は年齢や性別の嫌いなく応募できる。
This award can be applied for regardless of age or gender.