Complex sentence: Peterson states that he would not recognize the request of a student asked him to be referred to by a non-binary pronoun; he refuses to use anything other than "he" or "she" in reference to others.
Split into simpler sentences: Peterson states that he would not recognize the request of a student asked him to be referred to by a non-binary pronoun. He refuses to use anything other than "he" or "she" in reference to others.