Of course he says why they are wrong.
@Dawkins, Richard. The God Delusion. Boston: Houghton Mifflin, 2008. Print.
"THOMAS AQUINAS’ 'PROOFS’
The five ‘proofs’ asserted by Thomas Aquinas in the thirteenth century don’t prove anything, and are easily - though I hesitate to say so, given his eminence - exposed as vacuous. The first three are just different ways of saying the same thing, and they can be considered together. All involve an infinite regress - the answer to a question raises a prior question, and so on ad infinitum.
1 The Unmoved Mover. Nothing moves without a prior mover. This leads us to a regress, from which the only escape is God. Something had to make the first move, and that something we call God.
2 The Uncaused Cause. Nothing is caused by itself. Every effect has a prior cause, and again we are pushed back into regress. This has to be terminated by a first cause, which we call God.
3 The Cosmological Argument. There must have been a time when no physical things existed. But, since physical things exist now, there must have been something non-physical to bring them into existence, and that something we call God.
All three of these arguments rely upon the idea of a regress and invoke God to terminate it. They make the entirely unwarranted assumption that God himself is immune to the regress. Even if we allow the dubious luxury of arbitrarily conjuring up a terminator to an infinite regress and giving it a name, simply because we need one, there is absolutely no reason to endow that terminator with any of the properties normally ascribed to God: omnipotence, omniscience, goodness, creativity of design, to say nothing of such human attributes as listening to prayers, forgiving sins and reading innermost thoughts. Incidentally, it has not escaped the notice of logicians that omniscience and omnipotence are mutually incompatible. If God is omniscient, he must already know how he is going to intervene to change the course of history using his omnipotence. But that means he can’t change his mind about his intervention, which means he is not omnipotent. Karen Owens has captured this witty little paradox in equally engaging verse:
Can omniscient God, who
Knows the future, find
The omnipotence to
Change His future mind?
To return to the infinite regress and the futility of invoking God to terminate it, it is more parsimonious to conjure up, say, a ‘big bang singularity’, or some other physical concept as yet unknown. Calling it God is at best unhelpful and at worst perniciously misleading. Edward Lear’s Nonsense Recipe for Crumboblious Cutlets invites us to ‘Procure some strips of beef, and having cut them into the smallest possible pieces, proceed to cut them still smaller, eight or perhaps nine times.’ Some regresses do reach a natural terminator. Scientists used to wonder what would happen if you could dissect, say, gold into the smallest possible pieces. Why shouldn’t you cut one of those pieces in half and produce an even smaller smidgen of gold? The regress in this case is decisively terminated by the atom. The smallest possible piece of gold is a nucleus consisting of exactly seventy-nine protons and a slightly larger number of neutrons, attended by a swarm of seventy-nine electrons. If you ‘cut’ gold any further than the level of the single atom, whatever else you get it is not gold. The atom provides a natural terminator to the Crumboblious Cutlets type of regress. It is by no means clear that God provides a natural terminator to the regresses of Aquinas."