It's not about being nostalgic, genius. Language is a tool and its purpose is to be clearly understandable. You don't invite misunderstandings just to fit somebody's political agenda. In this sentence "the student lost their book" makes it somebody else's book and is thus a senseless linguistic failure.
@fvlasie - To make it correct what do you propose? "The student lost his or her book twice"? I'm curious, how would you correct the grammar and avoid the gender bias, which does not exist in the Korean, but would invariably creep into the English translation, unless you include "their" which is apparently endorsed by the Oxford dictionary to avoid that very bias. Looking forward to your suggestions.
@Blair - You object to "their"; so will you propose "his"? and someone else will object that the student is not stipulated as a male; then they will propose "her" and yet another someone will object that nowhere does the sentence mention a female student.... and on and on and on... When the subject is clearly singular; yet you find a "they/them/their" in the sentence, it should be obvious that that is done to avoid the gender bias.