Posted by Grant Richardson, 22nd August, 2015
To refer to a single person of unknown gender (i.e. male or female), you can use the word they. See here for examples.
In informal situations, the reflexive pronoun themself is often used (instead of themselves) to refer back to this person.
Anyone should be able to teach themself how to cook.
Perhaps this is because it sounds logically correct, being similar to myself, yourself, himself, herself etc., and perhaps because the correct reflexive pronoun of you (singular) is yourself, whereas for you (plural), it is yourselves.
So, logically, you would expect the correct reflexive pronoun for they (singular) to be themself; for they (plural), themselves.
However, most standard English dictionaries still do not list themself as a real word, and most spell-checkers will mark it as incorrect or try to autocorrect it to themselves. As languages evolve, perhaps it will one day be considered correct.
Macmillan Dictionary now lists it as a valid word, albeit with the caveat “Most people consider this use incorrect”: http://www.macmillandictionary.com/dictionary/british/themself
In the meantime, to avoid the possibility of being corrected or seen as a renegade (especially in formal situations such as academic or business writing), always use the reflexive pronoun themselves, and never themself. Of course,
Everyone can decide for themselves.