The argument is deductive, and follows the form of modus tollens.
1. If God does not exist, objective moral values and duties do not exist.
2. Objective moral values and duties do exist
3. Therefore, God exists.
To start here, AA attempts to simply get rid of the second premise by asserting that there aren't objective morals, but that morality is relative. AA cites a book that is explicating the history of slavery in the new world. The author describes briefly that St. Thomas Aquinas accepted some sort of slavery that was the basis for the attempted future enslavement of American Indians. Apparently AA is trying to imply that Aquinas was a-ok with slavery and this shows that objective morality is indeed an illusion. While I will shortly defend Aquinas' view, I must stress that this example does nothing of the sort. Simply offering examples of people who thought a certain moral abomination was morally good does not prove in any sense that morals are relative or that what that person did was right in any way. All showing past moral abominations does is show that moral abominations happened in the past.
Aquinas' view on slavery is far more subtle than AA is letting on here. Part of the reason for confusion is the ambiguous nature of the word "slavery." What exactly was Aquinas referring to? Aquinas is not referring to a slavery based on racial subjugation, but is referring to servitude in which one person has authority over another. Professor Hector Zagal from the Mexican Catholic institution, the Panamerican University, writes,
the Greek doulos, the Roman servus and the Medieval servus do not have the same meaning for the simple reason that the Aristotelic doulos is contextualized in a pro-slavery society and the Thomistic servus in a feudal society. We must not forget that feudal servitude is not equivalent to Greek slavery, since when Moerbeke translated for Saint Thomas the term doulos for servus, he was making a literal translation without considering the social context.1In other words, Aristotle's slavery (which Aquinas is analyzing) is not the same thing as Aquinas'. Zagal goes on,
Thomas considers servitude something just, yet he distinguishes two kind of justice: justice simpliciter and justice secundum quid. Servitude is not just simpliciter, since all men are equal by essence, even more since all men have been redeemed by the blood of Christ. Human nature is not predicable equivocally for every individual. Servant are as humans as their masters. Every man is truly a human person and, subsequently, is an individual substance of rational nature with an eternal destiny that is loved personally by the Creator. Attending to human nature considered in itself, all men are equal and, because of that, there is no preeminence of one over the other. The master as participant of the human nature has no domain over the servant. Servant and lord are essentially men.2
So Aquinas clearly didn't approve of the early American kind of slavery that atheists always anachronistically read into pretty much every historical setting.
AA then again reveals his ignorance about logic when he states, "This is a perfect example of my claim in my paper Against the Gods that just because all of your premises are true, it doesn't mean your conclusion is true, ie. god exists." AA needs to take an introductory class in logic. I do not say this to be mean or nasty or to insult him in any way! It is simply true. AA needs to understand how logic works. If the premises are true in a logically deductive argument, then the conclusion is true whether anyone likes it or not. That is why he needs to attack the truth of one of the premises. If he admits that the premises 1 & 2 are true, then he isn't an atheist.
He then immediately says, "This moral argument does nothing to prove god because there clearly is not any objective moral standard that we can call upon." Ok, so this is the premise he wants to attack; number 2. But this statement is baseless. It isn't clear that there is no objective morality. He says simply because most people believe in doing the right thing doesn't prove there's a god. No one is claiming that is how the argument works. The argument is deductive; unless there is a God, there is no right and wrong. Then he says that evolution created our moral intuitions. If that is true, then morality is relative, and saying it's wrong to kill babies for fun has no meaning. If morality is relative, then it's simply a matter of personal preference how one acts. Some people prefer to love their neighbors, others prefer to eat their neighbors. There's no moral value to any of those acts.
However, I think we all know that objective morality does exist. It's always wrong to torture people for fun, No matter what culture you're in. No matter what time period. As I've pointed out before any argument that can be given against objective morality, a parallel argument can be given against the external world. But I apprehend these moral realities just as I apprehend the reality of the external world. Why should I let those whose moral sense is deficient make me question the existence of an objective realm of morality? I don't question the external world's existence because there are color blind people.
He then moves on to the Euthyphro dilemma, which really hasn't ever been an issue for Christian theists, and Plato, who himself was a moral realist, in no way "demolished the moral argument." AA claims that splitting the horns of the dilemma by positing that God's nature is the good doesn't work, but then doesn't say why. He simply ridicules the notion. Sorry, AA, ridicule isn't argument. He says, "God is simply "good" by nature, and therefore he wouldn't command anything immoral? Right. Is that why many people have claimed to hear god speak to them, and they then commit horrible atrocities?" What does that have to do with anything? Because some people do evil and claim God told them to that proves God did it? Sorry, but the weakness of AA's argument here is glaring.
He then moves on to a better question. In essence, he asks if God is good, then how do we go about knowing this good nature? Well, we are made in God's image, so innately we would have some sense of what His moral attributes are. We can also find out what God's duties to us are from His special revelation in the Bible. AA mentions this, but then brings up the incidents in the Bible where God orders the killing of people. Why is this a problem for God? God says that murder, which is unjustified killing, is evil. If God commands someone to kill someone else, that killing is justified. God orders the killing of people for just reasons. God has the power over life and death, so while it is wrong for us to kill willy nilly, God can take the life of anyone He wants. I go into quite a bit of detail in this combox discussion.
In assailing God for these killings, AA has revealed that he actually does believe in objective morality. If he doesn't, then what is he complaining about what God did for? Maybe God just wanted to kill someone. Who is AA to tell anyone else what they are doing is wrong? After all, right and wrong really don't exist. He says, "Even though morality is relative, it does not mean we can do whatever we wish. We still have a responsibility to our friends and family and there are various secular moral systems that have been developed throughout history that can guide us through this morally relative world." If we have a responsibility to our friends and family, then AA has pinpointed a moral reality that is objective, unless he's willing to admit that this is not an objective imperative, to which I'd ask why he brought it up in the first place. If this family responsibility is objective, then by the deductive reasoning of the moral argument, God exists.
He says, "After all, even religion's morality is relative. It's dependent upon god's commands." He's either being dishonest or still doesn't get it. If morality is based on God's nature, then it is objective. It is a real reality that exists independent of any of us. If God created us, then we are obligated to follow His moral nature or face the consequences. Also, the moral duties God gives us are not arbitrary, but flow directly from His moral nature.
So, AA has shifted back and forth to wanting a moral objectivity when it comes to assailing God, to denying moral objectivity. But he's failed at giving us any reason to think morality is relative, he's failed at refuting the theistic response to the Euthyphro dilemma, and he's failed at refuting this argument in any way.
1 Hector Zagal, Aquinas on Slavery: An Aristotelian Puzzle, http://www.e-aquinas.net/pdf/zagal.pdf, 5
2 Ibid. 6