The best descriptor I read was that basically white privilege a the lack of negatives. Which can make it hard to perceive for some people.
Privilege is a loaded word, because it implies good, more, winning, ease of burden.... it implies a lot of things. And for the white kid who's born into poverty with drug addicted parents and no one teaching him right from wrong -- it's easy to look at a situation like that and say WHERE'S HIS WHITE PRIVILEGE? There's nothing about being white that is going to improve that situation for him. In that sense, you're right.
But if thats the only scope you want to view this with, you're being obtuse. That kid does not have the ADDITIONAL problems of higher incidence of punishment and expulsion from school , lowered job prospects, disproportionate police attention, harsher sentencing for the same crimes, and a slew of other fun stuff.
This is not to say that all white people are on the straight and narrow to success, and that no black people can do well via working hard. And there are other factors at play, as well. A black kid born into a wealthy family probably has better outlooks that the first white-kid example I created above. But don't close your eyes and pretend there's no difference in paths once all the other factors have been taken into account.