In your writing at Denver Seminary, you will be required to use gender-neutral language.
In older English, still used in some parts of the English-speaking world, generic nouns later referred to by pronouns used a form of the pronoun “he.” (E.g., “The student should bring his Bible to class.” Today, particularly in the United States, there are increasing numbers of individuals who find this kind of language archaic, confusing and/or offensive. There are ways, however, to avoid using the masculine pronoun in contexts like this, and thus make the language gender-neutral.
Good point about the continuing everyday-use of "man." I work in a highly secular, retail environment -- mostly twenty-somethings -- and I hear, not only "man" as a universal plural, but also "he"/"his" as a universal singular. E.g., "If a customer buys a Vista notebook, will he get the free upgrade to Windows 7?"
I never hear either "she" or "they" in everyday language. Only in academic papers.