を認めないだろう

probably won't admit

→ を
phrase Rare #32,595
probably won't admit Used after a noun to say that someone will probably not admit, acknowledge, accept, or approve of it. 認める can mean different things depending on context, while だろう expresses probability or expectation.
JA: 彼は自分の間違いを認めないだろう。
EN: He probably won't admit his mistake.

母は決して私の結婚を認めないだろう

My mother will never approve of my marriage.

彼は絶対に自分のを認めないだろう

He'll never admit his guilt.

彼は決して敗北を認めないだろう

He will never admit defeat.

父は決して私の結婚を認めないだろう

My father will never approve of my marriage.