I remember reading that "their" is third person plural, not singular. If you are talking about a student, most people would say: "The student opened their locker". If "their" is plural, then you wouldn't be able to use it. If you can't use "their", what do you use?
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This is actually an ongoing change in the language. People used to say "he" if the gender was unknown, but now we think of this as sexist. Some of the choices I've heard are "s/he" "he or she", "she" (used alternately with "he"). "They" seems to be emerging in usage, but I don't believe it's accepted yet in scholarly circles.
There are also the Spivak pronouns, but I think they are too alien to the language.
Personally, I'm a fan of singular "they" (singular possessive "their") and wish the language gods would get around to blessing it!