"Predicate nominative" is one of the phrases that has managed to stick with me for the more than 30 years since I studied Latin. (Thanks, Miss Draper!) When the subject of the sentence is equated to the noun in the predicate -- when they are defined as being the same thing with some variation of "to be" -- then the noun in the predicate will also be in the nominative.
It may help to think of it more like maths: "I = the man" (I am the man) is the same as "the man = I" (the man is I). (Mathematical symmetry.)