The use of his is sometimes taken to be "generic", i.e. to stand for a person of either gender, but I find this disingenuous. I have read studies where subjects were asked to write an essay about an individual, and were significantly more likely to assume the individual was male when the pronoun his (or he or him) was used. Furthermore, the generic he becomes less plausible the more likely the referant is to be female, e.g. few people would say "If a nurse is present then you should request his assistance." So, it seems clear to me that his/he/him is not generic after all, and indeed can sometimes inadvertantly discriminate against women by implying that they cannot hold certain positions in society.
Now, some sentences can be re-written so the referant becomes plural, thus avoiding the pronoun problem entirely, e.g. "All students should check their exam answers carefully." This is an elegant solution, however it isn't always available, e.g. it isn't easy to pluralise an instruction like "Have your doctor present [his? her?] conclusions right away."
Another option is to assign different genders to different individuals in a balanced way, e.g. "If a student is suspicious of his doctor, he should ask her for more information". But this adds an additional layer of complexity and implication where none is warranted, since presumably the characters' genders are completely irrelevant to the arguments being made.
Some have suggested inventing a whole new pronoun for the generic singular third-person. But it is very difficult to introduce a new pronoun into a language, and there is no consensus about what pronoun should be used, so I can't imagine this solution succeeding any time soon. Others use "his or her" (or "he or she" or "him or her"), but that quickly gets awkward and tiresome: "If a student wishes to dispute his or her grade, then he or she should ask his or her TA to assist him or her with formulating his or her complaint."
Thus, overall I am in favour of using the "singular they", whereby them/they/their are used when referring to singular objects of indeterminate gender, e.g. "Every student should check their exam answers carefully." It is true that this sometimes sounds awkward, but not overly so (to my ear), and presumably it would sound less awkward the more it is used. Some criticise this usage as being "ungrammatical", and indeed the editors removed it from a recent book that I wrote. But it does have historical precedent, including from William Shakespeare:
The use of the singular they isn't perfect. But in my opinion, it's the best option we've got. And, the more people that use it, the more common and natural-seeming it will become.