The climax of "Wiley, his mother, and the hairy man" occurs when

The climax of "Wiley, His Mother, and the Hairy Man" occurs when the Hairy Man realizes that he stole a pig, not a human baby.

Explanation:

The story of "Wiley, His Mother, and the Hairy Man" shows a very scared yet intelligent Wiley who wouldn't like to vanish on the hands of the Hairy Man, so he designs various approaches to keep himself safe and as the Hairy man needs to get him and remove him he falls into numerous stunts, for example, placing a pig in Wiley's bed, this makes Hairy man frantic since he needs to take that kid with him.