Aristotle has just shown that only genera and species of primary substances are secondary substances. He continues the Categories by explaining why no substance is ever in a subject.
It is a characteristic common to every substance not to be in a subject. For a primary substance is neither said of a subject nor in a subject. And as for secondary substances, it is obvious at once that they are not in a subject. For man is said of the individual man as subject but is not in a subject: man is not in the individual man. Similarly, animal also is said of the individual man as subject, but animal is not in the individual man. Further, while there is nothing to prevent the name of what is in a subject from being sometimes predicated of the subject, it is impossible for the definition to be predicated. But the definition of the secondary substances, as well as the name, is predicated of the subject: you will predicate the definition of man of the individual man, and also that of animal. No substance, therefore, is in a subject.
We already know that no primary substance is ever said of a subject nor is it ever in a subject. Secondary substances cannot be in subjects either. We say of a particular man that he is a man but we do not claim that humanity is somehow inside him. Neither is animality inside him either. There is a second reason that secondary substances are not in subjects either. The name of something in a subject may be predicated of the subject, but the definition of that name is never predicated. But the definition and the name of secondary substances are always predicated. Therefore, no substance is ever in a subject.
Next, Aristotle discusses an example of something that is not a substance but is not in a subject either.