What privileged position does an ordinary white male occupy? There are plenty of poor white men and plenty of rich privileged white women. Not every white man is Donald Trump or Rupert Murdoch.
That's the point - the average white male doesn't realise how good he has it. It's not about just wealth. It's about the assumptions that go with being white males. They have better opportunities, they are assumed to be more virtuous and productive than anyone who is a non-white, non-male (or any combination of those things).
This is why there's a pay gap between men and women of equal skill sets, and why less-qualified men are often promoted over more qualified women, or why less qualified whites are promoted over more qualified non-whites, or why non-whites viewed with more suspicion than whites.
Boiling this down to purely a money thing is too simplistic.
Our society is built on certain ingrained cultural assumptions that everyone has, conscious or otherwise. Some of them have fallen by the wayside as we have gone on, but the position as the white male at the top of that tree is the ongoing constant.
This doesn't mean that because there are examples of white males who are worse off than others that the system doesn't hold. You have to look at it on a large scale.
Now, what to do about that is a cause for some debate. I don't really have any answers, or feel like some of the proposed solutions are really adequate (for example, there are pros and cons to solutions like affirmative action that seek to address the ingrained hurdles that black people have when seeking employment that make such a system good in theory but at odds with a meritocracy in practice), but acknowledging that white male privilege exists is not controversial.