Nowadays, if you make such a Dawkins-is-uniformed argument, at least on the internet, you are likely to be told that something called "The Courtier's Reply" says all there is to say regarding your concerns. The brilliance of The Courtier's Reply has reached mythical proportions.
Of course if you haven't read it, don't make Dawkins's mistake of proudly arguing from ignorance. Pause your reading of this post and proceed forthwith to PZ Myers's classic essay The Courtier's Reply.
Got that? OK now I can tell you the I never understood the so-called brilliance of The Courtier's Reply. In effect it claims nothing more than this: there is no need to study the nuances or depths of something that is so obviously stupid (as theology). That's how the new atheists saw it. I always saw it as "don't bother doing any homework, just go ahead and make simplistic dumbass arguments, and we'll cheer you on as if you are a genius."
And, Richard H. Dawkins, isn't that precisely what happened? Dawkins repeated primitive and worn out platitudes such as "if God made everything who made God?" and The Courtier's Reply gave all Dawkinsdom license to declare that such unsophisticated, uniformed arguments were sufficient.
In the Church of Latter Day Atheists, the catechism, as justified by The Courtier's Reply, consists of just one question:
Q: What is the chief purpose of man?
A: The chief purpose of man is to agree with us. If he doesn't, he is stupid, stupid, stupid.
In the past era of the first-rate intellectual atheist, say Camus or Russell, Dawkins's arguments would have stood out for their inanity. Even the bizarre Ayn Rand made much more substantive arguments against religion. There is, for example, just a bit more anti-religion thoughtfulness in The Fountainhead during the telling of Rand's atheist-superman-protagonist's architectural commission to build a temple that in Dawkins's declaration of religion as child abuse. Intellectual atheists of the past paid no heed to the reasoning behind The Courtier's Reply. They would have recognized it for what it is: a declaration of anti-intellectualism. Instead, as intellectuals rather than anti-intellectuals, they studied, looked for weakness, sometimes subtle, and they tried to exploit those weaknesses. When debating, I suspect they often knew more about theology than their opponents. With Dawkins that would never happen.
The Courtier's Reply is license to wallow in ignorance--in fact it justifies, rationalizes, condones, encourages, celebrates, and rewards ignorance, simply by declaring the subject at hand (theology) is not worthy of study. I see that as laziness, not brilliance.