English lacks third-person singular personal pronouns that don’t connote gender. All we have are he, she, her, him, and it (which doesn’t work for people). So when we want to refer to an unspecified person without assigning a gender to him or her, we’re stuck with awkward, wordy constructions like him or her. In the past, writers used the male pronouns for unspecified people, but this is no longer acceptable as it can be interpreted as sexist. This creates a usage conundrum.
Reflexive pronouns are particularly problematic. For example, consider this sentence:
The patient must be able to take care of himself or herself.
The himself or herself construction is clunky and wordy, and few writers who value concision and euphony would want this sentence in their work. There are a few possible alternatives:
The patient must be able to take care of himself.
The patient must be able to take care of herself.
The patient must be able to take care of herself or himself.
The patient must be able to take care of themselves.
But there are problems with each of these options. The first two are gender-biased, the third and the original are clunky, and the last one uses a plural pronoun to refer to an individual.
Possible solutions
One solution is to always use the female pronouns, or to alternate female pronouns with male pronouns. This works in many cases, but it still calls attention to itself, and it can create confusion.
Another solution is to use the nonexistent word themself for reflexive pronouns. Spell-checkers will catch it, and it contains an internal contradiction (them is plural, and self is singular), but many writers hope it will catch on.
Finally, you can reword the sentence to eliminate the problem. For example, the writer could reword the above sentence this way:
The patient must be capable of self-care.
Or:
Patients much be able to take care of themselves.
Our opinion
We have opinions on this issue, but keep in mind that our opinions don’t necessarily reflect the prevailing views of actual English usage authorities.
(a) Formal and serious writing: When a sentence calls for a gender-neutral pronoun, word it in such a way that constructions like him or her are unnecessary. When rewording is impossible, use the wordy construction. If the wordy construction simply sounds awful, use a female pronoun.
(b) Informal and nonserious writing: In informal writing, use they, them, and their if they don’t sound too unnatural. Serious grammarians might not like this, but it’s a practical solution. In any event, the language is moving in this direction on its own.
So, in informal writing, there’s nothing wrong with these:
Any individual who thinks they can perform the job should fill out an application.
If anyone calls, tell them I’m out.
These days, everyone has their own website.
While these are okay, it’s still better to use he or she, him or her, or his or her where they aren’t too clunky and don’t call attention to themselves, where you need to be taken seriously, or where the alternatives might be confusing.