 There are two basic interpretations.  According to one interpretation, Aristotle does indeed include contradictions, but these are idle and play no real logical role in the argument he presents.  According to the other interpretation, following Aquinas’s commentary (lecture 20), Aristotle is not claiming that Callias both is and is not Callias or that he is and is not a human being, for example, but that the term “animal”covers Callias and those who are not Callias and not human beings, as Aristotle himself explains when he says that the major term (“animal”) is more extensive than the middle term (“human”).  (In the syllogism All As are Bs; All Bs are Cs; therefore All As are Cs, “A” is the major term and “B” is the middle term.)