... against the existence of God which runs like this. Life is incredibly complex, subtle and improbable. Therefore anything that designed it must be vastly more complex, subtle and improbable. But where could such a thing come from? Therefore there is no designer. Therefore God doesn't exist. Almost certainly.
However, it is a silly argument. Suppose life were so complex, subtle and improbable that it couldn't possibly have appeared by chance. That would mean it was definitely the product of a designer, and that designer would definitely be exceedingly complex, subtle and improbable - maybe infinitely so.
But where could such a designer come from? The very fact that life of this sort required a God would be the proof that such a God did not exist.
The flaw in the argument, of course, is that the necessity for such a designer to "come from" anywhere has not been established. Well, that about wraps it up for Dawkins. Perhaps he will go on to prove that black is white ....