… that I remember when gender was a property of nouns and pronouns (rather than a made up property of biological organisms) and that there were only four of them used in English: male, female, indefinite, and neuter. When using the English language, a person whose sex was known to be male was referred to as he, and a person whose sex was female was referred to as she. When referring to a person whose sex was unknown, the indefinite form one was used in formal speech and writing, and the masculine he was used informally.
Of course, English is a living language, and we now seem to have some noisy people who no longer are comfortable being addressed by pronouns which reflect their biological reality. However, this does not require coining new words. When speaking or writing formally about such a person, one can be used, and since we already have a perfectly good word for something that is neither male nor female, it should be grammatically correct for informal speech and writing about such a person. However, as of matter of respect for reality, I strongly prefer the use of the old masculine and feminine forms.
Note: The use of the plural form they is always wrong with referring to a single individual.
UPDATE—Stacy McCain deals with this issue from a different perspective here.