"He or her" x "He or she": Qual é o certo

Take a look at this video guys:
At 1:17 Bush says: "You teach a child to read, and he or her will be able to pass a literacy test."

My question is: Is there any reason that made Bush use "he or her" instead of "he or she"? I've never seen "he or her" before. Isn't that grammatically wrong? Would it be more correct if he had said "he or she"?

Thank you in advance!


PS: I don't know why the original poster of this video put that red box all over it. If you want to watch the video without that red box, just save it on your computer.