Please stick to ‘he or she’, or construct your sentence so that it does not require a gendered pronoun. For example (where the gender is not known) instead of: “He should not have done that”, you could try; “One ought not to do that”.

Actually, the history of the language for the past seven centuries supports the use of “generic ‘they'”. (See examples link at the end.)

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When you need to make a general statement of talk about a person of unknown gender, there are a few basic options.

1) “he or she” (him or her, his or hers) — this is a fairly recent addition. It may work in SOME cases, but in many others it is extremely cumbersome to use. I advise avoiding it

2) “he” (him, his) — used as a generic pronoun (NOT specifically masculine). Many people dislike using this form because it may seem to apply only to males, and even prejudice the hearers that way.

3) “one” (one’s) – singular and non-gender specific…. but unfortunately considered too awkward or stilted to use very much

4) “you” (your, yours) – works for SOME illustrations of things that might apply to the listener, but not for others

5) “they” (their, them) as a generic pronoun. This has the advantage of NOT specifying gender, which decreases chance of confusing it with the masculine or of offending someone.

Some people object (as you did) that they ‘cannot’ be correct because you want a SINGULAR. But if what you are after is a “non-gender specific singular” why is using a non-gender specific “plural” form somehow a bigger problem than using a masculine singular?

In fact, if used properly it will be very clear that you are using “they” as a singular, so there need not be any confusion. (For example, if it clearly refers back to a singular noun form. “If a writer uses the generic forms properly, their meaning will be very clear.”)

And, as I noted above, historic usage supports this option.

Since the 1300s (Middle English) many authors have used a generic “”they/them/their”. Note that this is just about the same age as the generic use of the masculine.

True, many grammarians fuss at this as inaccurate and a recent corruption, but the dates show that it is not a new thing, and numerous examples from the finest authors through the past 6+ centuries prove it is hardly ignorant.

For the history, a list of such authors and many examples (esp. from Jane Austen, about whom the page was written), as well as material from the Oxford English Dictionary, see the sections of the article “Jane Austen and other famous authors violate what everyone learned in their English class” beginning with:

http://www.crossmyt.com/hc/linghebr/austheir.html#X1a

“They” can also be used to indicate a collective. For example, you could use “they” when referring to a demographic group or political party.