The fundamental point is that if a writer has something interesting to say, you have to ask, sentence by sentence, if it is clear as it should be or could it be clearer, while also respecting the writer’s voice and tone. You have to listen carefully to the tone of the writer’s prose and try to adapt to it, but only up to a point.
Robert Silvers is describing the essential task of an editor. He should know what he’s taking about since he is the founding editor of the New York Review of Books, which is celebrating its 50th anniversary this year—and he stills edits the magazine. The quote comes from a long interview with Silvers in the April 15 issue of New York magazine.