Everyone who grew up lower-middle-class and ended up at a posh high school or college has stories of feeling out-of-place because they didn't know about arugula, because they had to work in the summers, etc. This is what "privilege" is generally in reference to, when everyone discussed comes from the West, from a background where at the very least they had enough to eat, but where within those limitations there's a wide, wide range of capital, cultural and economic, and this guy Bourdieu will tell you all about it.
There's also, however, the question of specific privilege - of the kinds of advantage that kick in only if your parents are in a field that's tough to break into and you yourself want to break into it. (See: the various Jagger offspring.) After being directed to Timothy Burke's don't-go that isn't really a don't-go, I got stuck at item two:
"For first-generation college students or students who have little familiarity with the hidden codes and assumptions of an elite liberal-arts institution, making it all transparent is absolutely critical."
(Not stuck-stuck, and I will probably have to post again re: interdisciplinarity.)
If your parents are not professors, if your parents are not professors in the field you wish to enter, you don't know anything. While being the daughter of a gastroenterologist has its benefits, and while my parents and some grandparents attended college, I can't say I grew up knowing the difference between funded and un-funded humanities PhD programs. Nor did I learn, from this, about how one gets tenure. Virtually everything I knew about applying to grad school came from having watched college classmates go through the process, from having asked college professors for advice. That's how I knew, for example, "[t]hat you don’t need to do a terminal MA first in one program as preparation for doctoral study." This is not some kind of ambient class-based thing, like knowing what Andover is or having a favorite painting at the Met.
And I screwed much of it up. I applied in what turns out was the wrong field (although thankfully the relevant dept. channeled me into the right one). I made appointments to meet important profs as I was still applying, something I learned only years later (via prof and grad student blogs, as it happens) is a major faux pas. I initially thought that I was going to grad school to write about French Jewish passivity during the Dreyfus Affair... only to learn that not only had this been written about a ton, but the (not-so-recent) book in which this argument was most famously made has been torn apart by every serious scholar in the field ever since. The obvious as well as the not-so-obvious have been pointed out to me over these past few years, or I've discovered them on my own. Cultural capital no doubt made it easier for me to figure these things out, and economic capital helped insofar as I did not have to pay for my parents' lives, just my own. But the idea that there's a class of college student really, really ready for academia is only true insofar as some college students are the children of academics.
Ultimately, I'm not sure how Burke's advice differs from Pannapacker's. While Pannapacker tells you not to go unless you're independently wealthy, Burke as good as says grad school's too risky if you're not the child of one but preferably two successful scholars in your academic area:
A student who loves literary criticism with a transforming passion but who has no idea how tenure works, where money comes from in a university, how scholars actually publish, what the big picture of disciplinarity is like, which famous literary critic is actually a notorious asshole, and so on, is heading for trouble at the exits if they decide to go to graduate school.Yikes. By that standard, nearly all advanced graduate students are in big trouble, and the few that aren't have been spending so much time researching the inner workings of academia that they might want to give their own research another look.
The question of how to make academia more accessible to those of all backgrounds is really two separate ones, one of which is about social mobility, the other of which is about making sure that the field is open even to those who were not discussing the obscure author who will ultimately be their dissertation topic around the dinner table growing up. Of course, if academia's as doomed as all that, the real question is how to find employment for the children of Comp Lit profs.