If we substitute he for they and his for their, the language police will still be after us, though on another charge: sexism. If we replace the plural pronouns with he or she and him or her, we could be booked on the charge of bad style (read the sentence out loud and you’ll hear why). If we switch to she or her,using these pronouns generically, we may be accused of eccentricity or even “political correctness.” According to The American Heritage Book of English Usage, only 3 percent of its usage panel supported using she and her generically (177).
Some writers have become so frustrated with pronoun agreement that they recommend throwing out the grammar rule altogether. “Why not allow they and their to be either singular or plural and be done with it?” they reason. Certainly, if we look at actual usage, especially in speech, we must admit that the grammar rule is broken all the time. Even in writing, the practice of pairing they with a singular antecedent is relatively widespread. According to The American Heritage Book of English Usage, “[This practice] can be found in such mainstream publications as Christian Science Monitor, The Washington Post, Discover, and Wall Street Journal” (179).
Despite evidence of current usage, few experts are prepared to abandon the rule. When presented with the sentence The typical student in the program takes about six years to complete their course work, 82 percent of a recent usage panel objected to using the plural pronoun their to refer to the singular noun student ( American Heritage Dictionary of the English Language 1796).
Many experts feel that the rule on pronoun agreement has a logical rationale worth preserving: Singular goes with singular and plural with plural. Barbara Wallraff argues that allowing they to be either singular or plural could lead to confusion, as in this example: 

"Is that the topic’s importance or the children’s?" writes Wallraff (32). The possible confusion is at first hard to see, but that’s because we all know that their, being plural, must refer to children, not to topic. If their can be either singular or plural, however, a potential ambiguity does arise: Their could refer to topic or to children. If we allow they to be either singular or plural for the purposes of pronoun agreement, what do we do about subject-verb agreement? Consider the following sentence:

 Assuming that the word they can be singular (to match someone), should we write “admitted that they was involved”? Let’s hope not! But allowing they to be both singular and plural in the same sentence seems a stretch: It defies logic. And how easy it is, after all, to fix the sentence:

As a matter of fact, adhering to the rule on pronoun agreement is not as difficult as it might seem. There are any number of effective revision strategies a writer might turn to. Consider, for example, three possible ways to revise the sample sentence given earlier:

Here are other strategies that will work at least some of the time.

Conclusion: There is little reason to throw out a perfectly good rule. With practice, writers can learn to satisfy everyone: the grammarians, the feminists, the stylists, and those who are annoyed by so-called political correctness.