DCTs hold that the reasons X is wrong is that God forbids X or commands us not to X; what makes X right is that God allows X; what makes X required is that God mandates X; etc.
The classic complaint is that God's commands--or lack thereof--are redundant or lack explanatory power. God must have independent reasons to forbid X, allow Y, or mandate Z. These independent reasons do all the work.
Imagine God had no such reasons to forbid this or allow that. This then renders morality arbitrary. It's like God took a list of possible actions, and then rolled a 1D6 to determine whether the action would be forbidden (1-2), allowed (3-4), or required (5-6). Rape gets a 1 and so ends up being forbidden. But God could have instead permitted or even required it. This account of ethics makes it look like the content is utterly arbitrary, and, further, that God's own actions are arbitrary. Unacceptable.
But if God instead had reasons to forbid this or allow that, it appears, then, that these reasons are what makes the actions wrong, permissible, or obligatory. The reason that God has for forbidding rape is also the fundamental reason why you should not commit rape. Maybe God's commands add something, but you would have reason not to rape even if no such commands were forthcoming, and even if God did not exist.
The key to divine command theory is to marry the idea of the good to another feature of a good ethical theory, that our obligations have a kind of social character. They obtain between agents. This idea is at the heart of contractarianism and contractualism, so why can’t divine command theorists avail themselves of it? For something to be obligatory, it can’t just be that a good God wants it to be obligatory; we need a divine action, a published directive, in order for the obligation to obtain. So our obligations derive from the combination of the idea of the good and the idea of obligations being social commands or directives.
Now Vallier goes on to say that DCT is bad because it provides the wrong kind of reasons. I owe it to Kevin not to kill him because of our relationship, not because of God's independent commands.
But I think it's worse than that. Contractualist theories face the same problems that DCT faces.
But, two, contractualist theories have the same kind of redundancy that DCT does. Contractualist theories usually are a variation of the following formula, which I take from Scanlon (1998, 153):
An act is wrong if its performance under the circumstances would be disallowed by any set of principles for the general regulation of behavior that no one could reasonably reject as a basis for informed, unforced, general agreement.
The general worry here is that the work is done not by this principle, but simply by the underlying reasons.
Why would reasonable people agree to principles? Because the underlying reasons are compelling. The reasons do the work. (If the reasons are not compelling, then why would reasonable people be compelled to accept or reject them?)
Why would hypothetical people sign a hypothetical contract? Because the underling reasons are compelling.
Why would the impartial spectator judge X good? Because of the underlying reasons or features of X.
Why would the virtuous agent do X? Because of the underlying reasons or features of X.
All these theories face the same problems. They cannot be fundamental moral theories.
In contrast, deontological and consequentialist theories talk about the actual reasons and features which makes things right or wrong, good or bad, virtuous or vicious.