For those who don't know what Euthyphro's Dilemma is, it is an argument sometimes used to prove the non-existence of God. I classify it as a materialist argument because it uses specifically the contingency of morality in the theistic scenario to disprove the existence of God.
We can express it as such :
If Divine Command Theory is true, then we have two options...
1. Are things good because God says they are good, or
2. Does God says things are good because they are good ?
Either option is self-destructive. If the Good exists because of God's fiat, then morality is subjective, and thus God cannot account for moral knowledge, which it must if it is Creator. If God decide on the Good because of some intrinsic property of goodness, then the Good already existed in the material universe, which once again is incompatible with God being the Creator.
The only reply presuppositionalists have to any materialist argument is to invoke the inherent-properties objection, and they do the same here. I hope you all know why this is wrong in all sorts of ways by now - see the relevant section in my Materialist Apologetics article for all the refutations. In the specific case of the Dilemma, there is no middle ground - either God is the origin of moral principles, or it isn't. If morality is an inherent property, then it is not chosen by God, and therefore falls on the second horn of the dilemma. Good already existed, and God is not the Creator of morality. In fact, God, in this scenario, is wholly irrelevant to the existence of morality.
You can see how Euthyphro's Dilemma is inscribed within TANG and the materialist approach that I propose. They are all founded on the contingency of material facts within the theistic scenario, including morality. If God can only exist in a reality where everything is contingent, and therefore subjective, to its will, then this cannot possibly be reconciled with a necessary, objective morality.
Furthermore, the subjectivity of the relation between God's nature and God's actions is another problem with the inherent-properties objection that I have never seen examined before, and would be worth discussing. I don't push this strongly enough in my own article. The problem is this : if every principle is contingent to God, then how can the theologian assume that God's nature, which he posits as necessarily logical (whatever that means), necessarily dictates its will ? In the case of human beings, for example, the fact of possessing logic does not dictate our will. So why should a god be so vulnerable ? Indeed, we can only assume this by removing the principle from God's sovereignty, which is, once again, a denial of the Creator property.
Now, why can't the Christian return the problem to us ? Let's do the flip side :
If materialism is true, then we have two options...
1. Are things good because we say they are good, or
2. Do we say things are good because they are good ?
And we end up with the same horns : either morality is subjective, or it is intrinsic and humans have nothing to do with it. In both cases it can be argued that materialism is ultimately defeated, if you are willing to push the point hard enough.
But in the case of human beings in a materialist scenario, we do have a middle ground. We do have facts to rely on, facts that are beyond our choice. We can drop things and measure their speed enough times to realize that masses attract - and give it the label of "gravity". We know inductively that when we drop a ball in a normal earthbound scenario, it's not gonna stay suspended in the air. This is not a subjective proposition, or an intrinsic one, but rather knowledge gained by observation and reasoning based on them.
To us human beings, living in reality, knowledge and the Good are neither personal nor magical. They are rooted in the determinism of this causal universe we live in and can understand. This illustrates the gigantic difference between the cartoon nature of the Christian scenario and the grounded nature of materialist reasoning. In short : nature left alone is solid ground, but nature dreamed by a Creator is an extremely simplistic and suicidal quicksand.
Where do we end up in terms of moral responsibility in the theistic scenario ? If morality is subjective, then there can be no such thing as moral responsibility, since there is no way to judge any action. And if morality is intrinsic, then moral responsibility can also be applied to God. Either possibility is fatal. Not only can we apply the Problem of Evil to the second case, but also the act of Creation itself. The fact that God creates anything can only imply that God was not perfect. If God was infinite and perfect, then the only possible moral action would be to do nothing at all. This thought was inspired by a very similar point made in "The Non-Existence of God", by Nicholas Everitt, which I recommend.