This practice began round about the time of the feminist movement in the late 20th century(c.1980-c.1990)
Taken from the Free Online Dictionary:
Usage Note: Using she as a generic or gender-neutral singular pronoun is more common than might be expected, given the continuing debate regarding the parallel use of he. In a 1989 article from the Los Angeles Times, for instance, writer Dan Sullivan notes, "What's wrong with reinventing the wheel? Every artist has to do so in her search for the medium that will best express her angle of vision." Alice Walker writes in 1991, "A person's work is her only signature."
Wikipedia notes why:
One response to this (use of generic pronoun he) was an increase in the use of generic she in academic journal
I've worked as a copy editor with numerous in-house style guides at different publishing houses, as well as with various style guides intended for a wider audience (Chicago, AP, MLA, Oxford, Words Into Type, Harvard Blue Book), and I can't recall ever having seen one that imposed an alternating-gender-pronoun approach. I have occasionally encountered this approach in books and periodicals, and have supposed that the author or publisher adopted it to emphasize the randomness of assigning gender to a person in a particular occupation or to a generalized human being, but I've never seen it required as a matter of house style.
The reason that it hasn't caught on as an approach to gender neutrality, I suspect, is that it has the effect of making gender more prominent in the course of a book or article. Whereas "he or she" or "she or he" or "(s)he" or "they" declines to assign a single gender to the hypothetical or representative person in a narrative, and indeed disposes of the issue of gender specificity by assigning both genders or neither gender to the working pronoun, the alternating-gender approach insists that each such pronoun—and the person it points to—is either male or female.
Rather than emphasizing (as I imagine it intends to) the interchangeability of male and female pronouns in generalized or hypothetical settings, it emphasizes that this first person is female, this second person is male, this third person is female, and so on. The reader is presented with an endless series of pronouns with alternating assigned genders instead of dealing with a text where gender assignment is avoided because it is unnecessary and irrelevant.
Undoubtedly, the distracting aspect of systematically alternating the gender of pronouns applied to generic individual people would diminish if the practice became the de facto standard in speech and writing, but even then I don't see how it would offer any meaningful advantage over the gender-neutral alternatives that are currently more common.
Best Answer
Singular they enjoys a long history of usage in English and can be used here: "Each student should save their questions until the end."
However, “singular they” also enjoys a long history of criticism. If you are anxious about being criticized (for what is in fact a perfectly grammatical construction) I would advise rewording to avoid having to use a gender-neutral singular third-person pronoun.
Some rewording strategies that can be employed:
OED References for “singular” they
Here for the benefit of those who lack access to its paywalled source are the full and complete operative senses from the Oxford English Dictionary. Per the OED the pronoun they has these specific subsenses for the various scenarios under discussion here:
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