I have seen many books and papers reference Athena breathing life into the man Prometheus molded out of clay, but I couldn't find any primary sources of this happening, and I couldn't find any good explanations. Why did Athena breathe life into the man Prometheus created?
Athena never did.
There was also an account, stating that Prometheus had created men out of earth and water, at the very beginning of the human race, or after the flood of Deucalion, when Zeus is said to have ordered him and Athena to make men out of the mud, and the winds to breathe life into them (Apollod. i. 7. § 1; Ov. Met. i. 81; Etym. Mag. s. v. Promêtheus).
So she was the one creating them with Prometheus, not breathing life into them.