Perhaps the most formidable of Darwin's critics was St. George Mivart. His major book, On the Genesis of Species, took aim at the notion that natural selection could account for the accumulation of the incipient stages of useful structures (Mivart, 1871). Stephen Jay Gould notes that
"Darwin offered strong, if grudging, praise and took Mivart far more seriously than any other critic...Mivart gathered, and illustrated "with admirable art and force" (Darwin's words), all objections to the theory of natural selection---"a formidable array" (Darwin's words again). Yet one particular theme, urged with special attention by Mivart, stood out as the centerpiece of his criticism. It remains today the primary stumbling block among thoughtful and friendly scrutinizers of Darwinism. No other criticism seems so troubling, so obviously and evidently "right" (against a Darwinian claim that seems intuitively paradoxical and improbable).
Mivart awarded this criticism a separate chapter in his book, right after the introduction. He also gave it a name, remembered ever since. He called it "The Incompetency of 'Natural Selection' to account for the Incipient Stages of Useful Structures." If this phrase sounds like a mouthful, consider the easy translation: we can readily understand how complex and full developed structures work and owe their maintenance and preservation to natural selection---a wing, an eye, the resemblance of a bittern to a branch or of an insect to a stick or dead leaf. But how do you get from nothing to such an elaborate something if evolution must proceed through a long sequence of intermediate stages, each favored by natural selection? You can't fly with 2% of a wing or gain much protection from an iota's similarity with a potentially concealing piece of vegetation. How, in other words, can natural selection explain these incipient stages of structures that can only be used (as we now observe them) in much more elaborated form?"
Gould goes on to point out that among the difficulties of Darwinian theory "one point stands high above the rest: the dilemma of incipient stages. Mivart identified this problem as primary and it remains so today."
Gould, S. J. (1985)
"Not Necessarily a Wing"
Natural History, October, pp. 12, 13