The "Burke quote" she uses here is a common but disputed attribution.
UN Speech on the HeForShe campaign (2014)
Context: You might be thinking who is this Harry Potter girl? And what is she doing speaking at the UN. And it’s a really good question. I've been asking myself the same thing. All I know is that I care about this problem. And I want to make it better.
And having seen what I’ve seen — and given the chance — I feel it is my responsibility to say something. Statesman Edmund Burke said: “All that is needed for the forces of evil to triumph is for good men and women to do nothing.”
In my nervousness for this speech and in my moments of doubt I’ve told myself firmly — if not me, who, if not now, when. If you have similar doubts when opportunities are presented to you I hope that those words might be helpful.
