What about the old adage that science deals with the "how" questions and religion deals with the "why" questions?
I think that's remarkably stupid, if I may say so. What on earth is a "why" question? There are "why" questions that mean something in a Darwinian world. We say, why do birds have wings? To fly with. And that's a Darwinian translation of the evolutionary process whereby the birds that had wings survived better than the birds without. They don't mean that, though. They mean "why" in a deliberate, purposeful sense. So when you say religion deals with "why" questions, that begs the entire question that we're arguing about. Those of us who don't believe in religion -- supernatural religion -- would say there is no such thing as a "why" question in that sense. Now, the mere fact that you can frame an English sentence beginning with the word "why" does not mean that English sentence should receive an answer. I could say, why are unicorns hollow? That appears to mean something, but it doesn't deserve an answer.
First, I think the question is put wrong. It's a common mistake. It should be What about the old adage that science deals with the "how" question and religion deals with the "why" question? Specifically, the question is about origins. Of humans. (We fundamentally seem to be chiefly concerned with ourselves.) Why are we here? How did we get here? This why question is what religion purports to answer. This how question is what science attempts to answer. That religion also has answers to the latter question is why creationists do not believe in evolution.
Additionally, Dawkins' point here is to say that some questions doesn't deserve an answer because putting the question that way solicits a certain kind of answer. An assumption has been made that atheists do not agree with, namely that there was a conscious mind that intended something with our creation. When you ask what the meaning of life is, then you are talking about someone deciding for you. If that works for you, then keep on deluding yourself by all means, in the face of all the evidence. I personally find it much more intriguing that the job of finding out why we are here is left to ourselves. It seems grand to me that our own conscious minds are the only entities that can decide what the meaning of this life is.