Discussions of privilege seem to be unsatisfactory, if necessary. There's no question that privilege exists, but it is just as true that the discussions of privilege are more often dead end name calling than paths to truth.
Perhaps the issue is that we tend to get sloppy about discussing exactly how privilege functions: privilege is only active in specific social contexts; otherwise, it is latent, it is potential. So, I exist privileged in several different ways: I am white, male, cishet, come from upper middle class, American, educated, etc. But, identifying privilege is only the start: figuring out how privilege functions is the important part.
When involved in a social context with white, male, cishet, working class fellows, I have class privilege even though, judged by my income and lifestyle, I am working class: even if I am currently working class, I have the privilege of my upbringing because, coming from an upper class family, I have access to privilege that my working class fellows do not (for example, coming from money, I will have more access to money should an emergency arise that I can not handle with my own money and/or credit). In a social context with upper class fellows, my current working class status elevates their privilege slightly over mine . . . though in the end, products of the same economic class end up having pretty much the same level of privilege, regardless of their current circumstances.
We can also imagine another specific social context (in academia, say) where a fellow's specific privilege my give them advantage over me even though they generally have less latent privilege than I do - maybe they are transgender, of color, etc. This privilege is limited to very specific contexts that are generally isolated from the center of power. Here, there is another level of dynamic at work: for not only are we analyzing how privilege works in a specific context, we are examining how that specific context fits into a greater framework of the social.
tl:dr; The problem is that we tend to think of privilege in its latent form as PRIVILEGE, when in reality we need to understand privilege as a social dynamic, and try to understand not only how privilege works in a specific social context, but also how privilege in a specific social context fits into a larger social framework of power and control relationships. AND THEN, we have to look at how these discrete events push back against and reshape the larger context . . . all this to say that privilege is a dynamic, not a state of being.