Put simply the argument from design looks at a sophisticated piece of machinery (a watch for example) and notices that it could not have come about on its own. It therefore concludes that the universe, which is infinitely more complex, certainly must have a creator.
Dawkins challenges this argument on two grounds, the positive and negative. His negative argument finds the flaw in the argument, that it only moves the question one step further back: Since G-d is even more complex, who created G-d? The positive rejection notes that universes and life are not like machines. Life is dynamic and came about slowly over billions of years. Watches can't build themselves, but millions of interactions over billions of years could rationally lead to human life.
Nagel takes issue with Dawkins' negative argument, arguing that he fails to understand its significance. He states that
If the God hypothesis makes sense at all, it offers a different kind of explanation from those of physical science: purpose or intention of a mind without a body, capable nevertheless of creating and forming the entire physical world. The point of the hypothesis is to claim that not all explanation is physical, and that there is a mental, purposive, or intentional explanation more fundamental than the basic laws of physics, because it explains even them.In other words, G-d works outside of the physical reality and as such is not subject to its rules. Hence he would not need to be created. I agree with Nagel that Dawkins' counterargument here is poor.
Nagel responds to the positive rejection by noting the complexity of DNA and how natural selection does not explain it adequately. For Darwinian natural selection to have come about, the organisms subject to mutations (ok maybe not the word Darwin would have used) must have a type of genetic code which allows for mutation. But how did something as complex as DNA come about?
Even Dawkins notices the problem. His answers (according to Nagel) are basically the anthropic principle (that there are billions of possible worlds and our world ended up being the lucky one). Not a very good answer.
Nagel's best point comes at the end of the article. He focuses on how scientists, especially afraid of how religion curtails scientific thought, have searched for a physical answer for everything. The philosophical dispute about Materialism is based on this point. Is there a physical source for our thoughts, desires, and ideas?
Assuming that we can use "reductive physicalism" to answer all of life's questions is a fallacy. As Nagel puts it,
This reductionist dream is nourished by the extraordinary success of the physical sciences in our time, not least in their recent application to the understanding of life through molecular biology. It is natural to try to take any successful intellectual method as far as it will go. Yet the impulse to find an explanation of everything in physics has over the last fifty years gotten out of control. The concepts of physical science provide a very special, and partial, description of the world that experience reveals to us. It is the world with all subjective consciousness, sensory appearances, thought, value, purpose, and will left out. What remains is the mathematically describable order of things and events in space and time.
That conceptual purification launched the extraordinary development of physics and chemistry that has taken place since the seventeenth century. But reductive physicalism turns this description into an exclusive ontology. The reductionist project usually tries to reclaim some of the originally excluded aspects of the world, by analyzing them in physical--that is, behavioral or neurophysiological--terms; but it denies reality to what cannot be so reduced. I believe the project is doomed--that conscious experience, thought, value, and so forth are not illusions, even though they cannot be identified with physical facts.
Nagel is right. There is no evidence that science can solve all of life's problems. It's a method that works well to describe the physical reality, but is no more qualified than religion when answering metaphysical questions or searching for epistemic truths.