Divine nature theory is what I call the common theistic meta-ethical opinion that goodness is grounded in a likeness to God's essential nature. God is essentially loving and kind and just, which is taken to explain why it is good to be loving and kind and just and so on.
But there is an obvious counter example to the theory as so far construed: God has many essential characteristics that are not morally significant. God is essentially immutable, necessarily existing and ontologically self-sufficient. But it would be absurd to say that something was good in virtue of its being immutable, necessary or having aseity.
The divine nature theorist might try to revise his view, saying instead that a thing is good just in case it bears some resemblance to God's essential behavioral qualities. Necessity, immutability and aseity have nothing to do with behavior, and so they pose no threat to this view. And yet, other counter examples can still be raised. God is essentially rational, prudential, decisive, and is essentially not impulsive or whimsical. But it seems silly to think that being irrational or imprudent would have any affect on the moral value of ones action.
The divine nature theorist might take a further step back, saying instead that a thing is good just in case it bears some resemblance to God's interpersonal behavioral qualities. Being rational doesn't have anything to do with how one treats others, but lovingness and kindness and justice does.
But now there's an even more pressing problem, in that these qualities don't seem like essential characteristics of God. God cannot be necessarily loving or just, since there are no other necessarily existing people to be loving or just towards. Some have suggested positing the trinity to solve this very problem, saying God's persons necessarily love each other. But love is just one of many morally significant properties the theist is trying to ground in divine essence. What about other morally significant behavioral qualities, like being someone who punishes the wicked, or who protects the defenseless? There are no necessarily existing wicked or defenseless people for God to stand in the appropriate interpersonal relationships with.
The divine nature theorist might try one last revision. He might suggest that goodness is grounded not in any qualities God actually has, but in counterfactuals about what God would do given the opportunity. And so protecting the defenseless is good because, given the opportunity, God would always protect the defenseless.
But now the divine nature theorist has made God entirely dispensable to his theory. Even atheists can believe that, if God were given the opportunity, then he would protect the defenseless. Divine nature theory, then, reduces to something very much like ideal observer theory, and is no longer an inherently theistic account of goodness.