No topic in English usage has received more attention in modern practice than the lack of a common-sex third-person singular pronoun. For most of our language’s history, he dealt with all such matters: He who is anyone knows me, The student must complete his test, Let no one leave without his pay. These phrases have obvious masculine implication that, whether we want to admit it or not, ignores female involvement.
Unfortunately, English only has three third-person singular pronouns: he, she, and it. Writers have suggested adding a common-sex pronoun like thon, heshe, hse, hu (human), per (person), himorher, ha, and shiz, but none of those have ever caught on. I have occasionally seen the abhorrent s/he, which has the sole effect of forcing readers to stumble over the slash and decide halfway through how to pronounce the word. Do not impose upon the reader the task of your expression.
Many writers want to use the colloquial they for the singular pronoun. H.W. Fowler calls it horrible and Bryan A. Garner resigns to its popularity, but the use of they for he or she is grammatically wrong. At the expense of number, they also risks confusion: The child went to the zoo and watched the penguins, and they clapped with great joy. To whom, if we accept they as singular, does they clapped refer? And if we accept they as singular, should verbs agree with the singular subject or the plural pronoun? The person must decide if they wants to listen is correct if they is a singular pronoun, but it sure doesn’t sound correct. They does not solve the problem; it only introduces new ones.
The most popular alternative, he or she, may work in most situations, though overuse of he or she creates bloat, slows the reader, and can suggest two people are involved rather than one. The astute reader may also ask why we say he or she and not she or he, which reminds us of the original issue.
Where does that leave us? We could accept he and man to mean also the general human being—one of the definitions for man in the Oxford English Dictionary. But while he falls invisible to readers like myself, there are plenty for whom it causes discomfort. Thus my best suggestion, which echoes most style guides, is to rewrite your prose to avoid the pronoun. Often the singular can become plural, though plural feels less intimate: If my reader disagrees, he can shove off becomes If my readers disagree, they can shove off and Let no one leave without his pay becomes Do not let them leave without their pay. Where the plural doesn’t work, consider rephrasing to avoid the situation altogether; the lazy writer may complain, but, as an example, this dictionary’s many entries do not use singular third-person pronouns except in examples. My second-best suggestion is to switch singular pronouns between works: one essay, she, the next, he, and so on. It is conscientious even if it doesn’t avoid the problem at hand.