On Friday evening, journalist Caitlin Moran trailed her big Saturday interview with actor and screenwriter du jour, Lena Dunham, on Twitter. Someone named @lizziecoan replied to ask: "did you address the complete and utter lack of people of colour in girls in your interview? i sure hope so!" Moran's response: "Nope. I literally couldn't give a shit about it." By Sunday morning, blogs were being written about this exchange, and discussions about the nature of modern feminism had once again become the topic of the day.

How do you define yourself? The very essence of you? There are things that we all share: our body chemistry means we breathe air and drink water and produce waste. After what we have in common comes what is inescapably different: the things that come with the geography of the place we were born, the amenities we have access to, how much money is in our wallets, the colour of our skin. We are more than checklists, sure, but we are also the sum of our various "parts".

Here are mine: I am a woman, a black woman born in London to Nigerian parents, a Muslim woman (who does not wear a hijab or veil). I am educated and self-employed but relatively low-earning. These things, as standalones or collectively, define how I see the world. One often bleeds into the other so comprehensively, they seem almost interchangeable. This is, in its most basic form, what we call intersectionality: the idea that we wear a lot of caps, and often in challenging one wrong, we are challenging many. In reading that Moran tweet, my first thought was: "I cannot afford to take off my 'race cap' and focus just on the plain ol' sexism that plagues the television industry; and nor do I want to."

The feminism I learned about was very much of the intersectional sort. Most of the feminism theory I have read and understood has been self-sought and self-taught. My father told me of Funmilayo Kuti as a child; a decade ago, I read bell hooks and Linda Bellos, and more recently, Audre Lorde. I follow Feminist Ryan Gosling and read blogs, and use them as a jump-off point to plug the holes (of which there are still many) in my knowledge and understanding. It is the feminism that was summed up by feminist writer Flavia Dzodan, when she wrote: "My feminism will be intersectional or it will be bullshit."

I was one of the people who took to Twitter to talk about Moran's reply. Over a series of posts, I extracted what I considered to be the kernel of my discontent with the exchange: the unchecked and damning privilege that emanated from Moran's tweet.

Some caveats: I've followed Moran from about the second day I joined Twitter. I find her writing funny (she has a great gift of the gab) and sometimes insightful, and I think there are subjects on which she has produced remarkable journalism. But I think she embodies a certain kind of feminism, the feminism that is mainstream commonsense: women should earn the same as men, they should not suffer in the career stakes when they go off to have babies, they should be able to have sex as plentifully (or as little) as they want with no shame or opprobrium etc.

Where this feminism often falls down is in its ability to be intersectional. My theory is that Moran's flippant tweet response was in keeping with the general tone of her Twitter feed: no crime there.

But what it betrays (an ignorance of crossover interests) was soon echoed by the people who stood up to defend her: there were calls to stop "in-fighting", to focus on "more important issues" like abortion and the general bringing down of the patriarchy. That attitude is irritating and perfectly encapsulates the silo-thinking of so many feminists.

The criticism of Dunham has been harsh, because whether through the media blitz of publicity or the often-taken-out-of-context assertion that she is "a voice of a generation", she is a highly visible woman purporting to tell the stories of contemporary women. The same – slightly modified – goes for Moran: her book, How To Be A Woman, was feted as a feminism handbook of sorts, and she self-identifies as a feminist.

When we have "heroes", we look up to them, and feel it especially keenly when they mess up. But even with all of my affection for the series, the omission of black and brown people in non-stereotypical roles was glaring. Is it unfair to ask Dunham to represent all of womanhood onscreen? Of course it is. But here's the thing: no one did. We merely asked that she take a step back and question the underlying reason for why Girls looks the way it does. We asked it of Friends (well, I did) and Sex and the City and Seinfeld. We have the right, as consumers of pop culture to make a noise.

I liked Girls. It wasn't perfect by any means, but it was engaging and funny. No one wants to get caught up in the "Oppression Olympics". But if women of colour (don't know what that is? See here) are telling you there's a problem, do not consider it to be an attack purely for the fun of it. Stop, listen, try a little intersectionality on for size. Don't belittle my valid concerns by framing it in the grander discourse of "fighting the patriarchy". If I am telling you that I have a migraine, don't tell me to focus exclusively on the gangrene eating away at my leg. There's time to treat both, no?