The question admits no simple answer. Moreover, only by an effort can one disentangle the answer from politics, and even then not wholly. Nevertheless, let us make the effort and try.
Why to prefer he
On the one hand, English is a Germanic language, which means among others that it has never sought a complete set of unambiguous pronouns. A Germanic language distinguishes pronouns extensively by context. For a famous example, consider the modern German sie, "she," and Sie, "you" (formal), the two words capitalized differently (though not so at the beginning of a sentence) but always pronounced alike. Whereas in English, it is she that has her own, distinctive pronoun; in modern German it is er, he.
Clumsy? Maybe. But that's Germanism for you, with roots as deep as Herodotus' tales of the frozen forests of the dim, Germanic north. You cannot alter the essential way the Germanic languages approach pronouns but by uprooting the language family entire. The pattern is etched in the languages' bones.
At any rate, on Germanic grounds, the preferred pronoun in the sex-indefinite semantical singular would be he.
Why to prefer they
On the other hand, unlike modern German, English does admit a peculiar but nevertheless respectable, centuries-old alternative to he in the sex-indefinite semantical singular. This alternative is they.
The use of they in the sex-indefinite semantical singular is admittedly soft because it thrashes English grammatical number—as in, "A ship's captain is responsible for everything that happens on board. They are not allowed excuses." Fortunately, the practical use of they in the semantical singular usually (though not always) proves more congenial than in it does in contrived examples like the one I have just given. Unobjectionable examples of the following kind are rather more typical: "Each writer will choose the pronoun they think suits the context." (You might still prefer he, which is fine; but one cannot characterize they as wrong here.)
Both alternatives for the sex-indefinite semantical singular, he and they, have long been attested by good writers. Both can and probably should be used, even in the same literary work.
The use and misuse of she
In recent decades, we have sometimes seen less good writers force she into the role of the sex-indefinite semantical singular. This fad represents not English style but political agitprop and should never voluntarily be done except to achieve a specific political effect. Use he or she rather, if you must, as the emphatically sex-indefinite semantical singular.
You will hear some good writers deprecate the three-word pronounal he or she, but you should understand what they probably, actually mean—and do not mean—by deprecating it. It is doubtful that a good writer deprecates he or she when the sex-indefinite nature of the pronoun calls for particular emphasis. Moreover, it can hardly be contested that today's world (for better or for worse) furnishes more subjects than formerly that call for he or she. Still, most sex-indefinite subjects do not want such emphasis, and he or she is admittedly overused.
Regarding plain she, whose use we said was forced, we should note that not all uses of she in the sex-indefinite semantical singular actually are forced. One can use she rather than he when the sex referenced is only quasi-indefinite, understood probably to be female.
As a default, prefer he to they for the sex-indefinite semantical singular, on the ground that Engish is a Germanic language and that he represents the better Saxon/German.
Though we have not yet mentioned it, on the uncommon occasion on which the matter arises, consider preferring she to it as the pronoun of personification (advice I have not actually followed in the answer you are reading, if only because I did not wish to distract the topic by beginning, "English is a Germanic language, which means that she has never sought a complete set of unambiguous pronouns").
In a college course, of course, the wise student will avoid bucking the instructor's sensibilities in the matter, whatever these sensibilities may be. Even in the unlikely event that all you learn during the four months of the course is that you and the instructor disagree, by having given the instructor's way a fair trial, you will have established a sound, respectable right to your contrary opinion. You will also have earned a high grade in the course.
Regarding language and politics, see Orwell, George. Nineteen Eighty-four.