For me, learning about privilege helped me to put myself into context. l realized that my feelings of unease at being called bossy when I didn't feel like I was any more bossy than the other kids who were taking charge (boys) were not necessarily just problems with myself, they were in part manifestations of larger patterns that all women had to deal with.
A similar transformation happened in college when I heard people talking about double standards for women; I had been struggling to figure out how to not be a prude and also not be a slut (and also not a tease). No matter what I did I seemed to fall into one of those categories. Every girl I knew had been called at least one of those terms, and we all took it personally, as if it were really an attack on us and we should reflect on it and change our actions. Well, this doesn't mean that we should brush it off and any criticisms of our sexual tendencies or our leadership abilities are simply sexism, but it does mean that we can trust our own feelings of what feels right a little bit more, since we know that generally, people's perceptions are a little bit skewed in certain ways.
And because I'm totally white, I never had to deal with racism, and naturally, didn't acknowledge that white privilege existed (or if it did, it was miniscule and really not worth worrying about). I grew up in a good neighborhood and thought that if everyone did their part and tried to be good people, that would be much more effective than teaching about sociological constructs.
I think the same idea applies here, and to every privilege. Learning about privilege should not be a way to devalue the actions of those in power. It's not about the people in power, it's about the people not in power. That's perhaps why it's a problematic word; it draws attention to the wrong side of the equation (or, inequality I guess).
The point is, when black students are taught in school that the language that they use at home and at church with their loved ones is "incorrect" English and they are marked down for it and labeled "bad at English," that's reflective of the power dynamic, not of them.
Realizing that language is actually always evolving and that linguists would never say that there is a "right" way and a "wrong" way to speak, rather it is the existing power structures asserting their dominance through language that makes one way "right" and one way "wrong," empowers those who are in the position of less power to understand their place in society for what it is, and to claim agency and, if they so choose, learn the dialect that those in power deem to be correct so that they may enjoy more privileges than they currently do.
It's giving the people crushed by the system a map of the structure of the system, so that they can stop blaming themselves and climb up the hierarchy and break the cycle of living self fulfilling prophesies. (While it won't solve the larger problem of our systems being based on power imbalances, it will at least help the imbalance be a little more equally spread. Ideally once people achieve more privilege they will use it to help others and not just disconnect from their past, but this comes through true awareness of the system. If anyone knows of an alternate system in which inequality is not to some degree inevitable, let me know).
And there are all kinds of other privileges that are not in the typical canon. There are other power dynamics that are responsible for which are talked about and which aren't. That's empowering. Now that we know that, we can talk about any privilege that personally bothers us, and spread that understanding to those that need to hear it most.
So if you find yourself in a Facebook comment war about whether privilege exists, simply bow out as politely as you possibly can. The people who deny the existence of privilege or its severity are not going to change their minds because of a comment thread. But keep posting and spreading awareness, because it's reaching the people who really need to hear it that will have a positive effect on society. The people who need to hear it won't fight you on it, they'll appreciate it.