When two or more reasoned intellectuals, after lengthy discussion, still disagree, there are a couple of possibilities.
1) Their starting "definitions" related to what they are discussing differ. Their different conclusions can, in this case be completely attributed to their starting definitions (Technically it is their initial AXIOMS (ie. starting assumptions) that differ that are IMPLICIT in their "definitions" that generate their conclusions through logical processes)
2) The data they are using is in dispute or otherwise differs between them.
X) One of them is not being reasonable or is not intelligent enough to see the obvious logic or illogic.
X) can be discarded because we are talking about reasoned intellectuals see initial definition.
If in this case we are talking about me and Dawkins (with his reasoned intellectual hat on as opposed to his ridicule the opposition hat), it really is just (1). These are the definitions of his that differ with mine at this stage:
a) The in-principle provability or disprovability of God.
b) The definition of God that will allow himself to be tested.
c) His definition of "Design".
d) His definition of "Religion".
I have a choice when reading the book to set aside these differences by taking on his definitions and concentrate on his logic - or ignore any conclusions that can be attributable to the differences in our definitions. Atheists in general take on definitions that are accepted by the majority of naive christians, that wouldn't pass muster with any intellectual theologist or philosopher.