The new "Sex and the City," in case you missed that.
So what is she, then? A decadent anti-hero? A George Costanza for our times, who represents the worst in all of us, our worst fears? (That a wide-ranging commentariat has seen us naked and isn't impressed, and that we come across as entitled.) Given that the near-entirety of mainstream show business is white people with family connections, we might also ask why someone whose connections aren't even in show business, and who, while white, lacks the specific kind of whiteness-privileged possessed by Gwyneth Paltrow, Angelina Jolie, Kate Hudson, and whichever other famous-daughters-of-famous-people, namely fitting the most conventional beauty standards possible... why such an individual inspires such YPIS. Is the problem that Dunham presents herself as ordinary? Is it somehow offensive to audiences that she doesn't acknowledge her native-New-Yorker privilege by getting her hair done at Bergdorf's? Why is she, of all performer-creators, the one asked and asked again to step aside on behalf of someone more deserving?
I might take this even further, and consider how critiques of systematic unfairness often end up punishing relatively powerful intermediaries rather than those in the positions of greatest power. This happens with NYC schools - however valid both questions may be to investigate, it's much easier to ask why elite public schools are predominantly (lower-?) middle-class and Asian than to ask why private schools serve wealthy white families. Similarly, someone like Dunham, whose status is more precarious, who frankly wasn't born into stardom, just posher circumstances than most, is easier to pick on than someone like Kate Hudson. (Paltrow, with her lifestyle-empress aspirations, is another matter.) And yes, I do get the sense that people consider it unfair that a young woman got so successful so fast for reasons other than her physical desirability. (Not that she's undesirable, just that her talent/self-promotional ability seems more the issue.) There's this sense that there's a natural order of things - of course rich white kids go to the actual fanciest schools, and of course the pretty daughters of movie stars are box-office sensations. These things we just accept. But when someone shakes things up from the middle, or upper-middle, there we can unleash whichever populist outrage.
The above are most decidedly not my fully-formed thoughts on this. But if my musings inspire musings of your own, comment away.