This is the 3641st most frequent Japanese word.
食わ
"食わ" is the stem form of the verb "食う" meaning "to eat" in casual or colloquial Japanese.
The word '食わず' is used here as the negative form of '食う,' meaning 'don't eat.' It emphasizes what he avoids eating.
彼は魚を食わず、肉ばかり食べる。
He does not eat fish; he only eats meat.
The word '食わない' is the negative form of '食う,' indicating a refusal or dislike of eating vegetables.
その子供は好き嫌いが多くて野菜を食わない。
The child is picky and does not eat vegetables.
The term '食わなかった,' derived from the verb '食う,' figuratively represents the unwillingness to 'accept' or 'swallow' the proposal.