If privilege were simply knowing that one has advantage, it would be as easy as saying “I have money in my pocket.” I do. Some don’t.
The difference lies in the way people use these labels. Few would say that I owe them something on the basis of me having money in my pocket, and if they want some of it they typically offer something in exchange, or ask it as a gift. Not so with white privilege. The phrase “white privilege” is used almost exclusively to demand. “You have white privilege, therefore you must accept my stance or values and I may freely disregard yours.”
I can easily accept the idea that I am privileged because I am white. This has never been a struggle for me, the way it was a struggle for Elizabeth and the target audience of her essay, because I am conservative: I do not believe that if a person has, that person necessarily owes to those who have not.