I don't like eggs.

Literal

Egg [topic-は] disliked is.

嫌い is a na-adjective meaning 'disliked / hated,' taking だ/です copula. Critically, the subject of 嫌い is the 'liker' (usually omitted), and what's disliked takes は or が — the opposite mapping to English 'dislike.' Japanese routinely expresses preferences this way: 好き/嫌い + が for the object of the emotion.