What's the correct usage when you're referring to people that could be either gender?
The exclusionary tradition was "he/his" regardless of whether or not it referred to something that included women.
Some people suggested using only "she/her" for a hundred years or so to even the score but that didn't catch on.
The grammatically correct "he or she, his or her" works but can get awkward when required too often in the same sentence: "When a student leaves for college, his or her parents can be upset about his or her departure and miss him or her dreadfully." (OK, there are less clumsy ways to say that, but you get the idea.)
Some writers alternate, using "he/his" in one sentence and "she/her" in the next. Not great because you tend to make a mental picture of the first person referred to and it feels a bit strange when the next sentence refers to a person of a different gender.
Often the plural is a good solution: "When students leave for college, their parents..."
Even when referring to one person some writers use they/their: "When a student leaves for college, their parents..." To folks who were brought up to think of "they/their" as always plural this is jarring but this solution is gaining on the others.
Whichever one you choose, the important thing is to be consistent, unlike this example from a USA Today article by Mark Saltzman:
"No one wants his tech running out of steam before they do."
He starts out with "his" and switches to "they," which is especially confusing here because, reading quickly, it sounds like "they" could refer to "tech" as well.
Another sentence from the same article confirms that USA Today is sticking with their "we don't bother to edit columns" policy:
"If interested, the app also synchs audio at the same time as your notes, perhaps recording what the teacher or professor is saying."
What gets the app interested? And when something synchs with something else, "at the same time" is by definition. The "perhaps" makes it sound like the app may or may not decide to record what the professor is saying. I guess it depends on its mood.
I'm not trying to be overly hard on Mr. Saltzman--I'm sure he could find lots of errors on this blog--but when something goes out in the name of a national newspaper (even a newspaper-lite like USA Today) you'd think they'd have an editor give it at least a quick look.