The stars are not for man.
This quote is from Karellen, in Chapter 14. Karellen gives it in a press conference, after showing the reporters a holographic projection of the galaxy, with its "thousands of millions of stars," and asking them, rhetorically, whether they thought mankind could handle so many worlds. This statement is later agreed with by Jan Rodricks, the human who so wanted to get into space. The reason the statement is important is because it is so out of line with all of Clarke's other writings. When the paperback edition of Childhood's End came out, Clarke added a warning in the front: "The opinions expressed in this book are not those of the author." One of the "opinions" he is referring to is undoubtedly this one. Almost all of the rest of Clarke's fiction supports the idea that Earth is just a frog pond where humanity is currently growing and developing but will eventually leave by reaching out to the stars.
So why, in this book, does Karellen say, "the stars are not for man?" This may be the result of the mythological and folkloric framework that Clarke used as the basis for Childhood's End. More than most of Clarke's novel, Childhood's End draws on allegory: the Overlords are Satan and his rebel angels, the Overmind is a God-like figure, and the assimilation of the children into the Overmind is the Rapture and Armageddon rolled into one. Saddled with his conception of a science fiction version of Armageddon, Clarke is almost forced to have the Overlords shut heaven off to mankind.