I’m a pretty strong atheist. It’s odd to me too. However I’m answering why the Bible over other religious texts. That one at least feels obvious.

The people reading it were likely Christian. The majority of the people listening would’ve been Christian. The majority of the people that footed the bill would’ve been Christian.

Like others have said, you don’t have to believe in the existence of a diety to feel moved by words from some religious texts.