The word subject has different uses in logic. In “Zayd is learned,” Zayd is the subject of a proposition: the assertion is about him.
In “Whiteness inheres in cloth,” the cloth is the bearer of the accident. In the definition of the categories, “in a subject” refers to this second meaning, not to every noun that could serve as the subject of a sentence.
Without this distinction, one might incorrectly say that paper must be an accident because “paper” is the subject of “paper is white.” The paper is the body; whiteness is the accident.