FYI here's an overview of the topic discussed yesterday:
http://www.iep.utm.edu/d/divine-c.htm
See especially
3. A Persistent Problem for Divine Command Theory: The Euthyphro Dilemma

relationship between God and ethics. In this dialogue, written by Plato (1981), who was a student of Socrates, Euthyphro and Socrates encounter each other in the king’s court. Charges have been brought against Socrates by Miletus, who claims that Socrates is guilty of corrupting the youth of Athens by leading them away from belief in the proper gods. In the course of their conversation, Socrates is surprised to discover that Euthyphro is prosecuting his own father for the murder of a servant. Euthyphro’s family is upset with him because of this, and they believe that what he is doing—prosecuting his own father—is impious. Euthyphro maintains that his family fails to understand the divine attitude to his action. This then sets the stage for a discussion of the nature of piety between Socrates and Euthyphro. In this discussion, Socrates asks Euthyphro the now philosophically famous question that he and any divine command theorist must consider: “Is the pious loved by the gods because it is pious, or is it pious because it is loved by the gods?” (p. 14).

For our purposes, it will be useful to rephrase Socrates’ question. Socrates can be understood as asking “Does God command this particular action because it is morally right, or is it morally right because God commands it?” It is in answering this question that the divine command theorist encounters a difficulty. A defender of Divine Command Theory might respond that an action is morally right because God commands it. However, the implication of this response is that if God commanded that we inflict suffering on others for fun, then doing so would be morally right. We would be obligated to do so, because God commanded it. This is because, on Divine Command Theory, the reason that inflicting such suffering is wrong is that God commands us not to do it. However, if God commanded us to inflict such suffering, doing so would become the morally right thing to do. The problem for this response to Socrates’ question, then, is that God’s commands and therefore the foundations of morality become arbitrary, which then allows for morally reprehensible actions to become morally obligatory.

Most advocates of Divine Command Theory do not want to be stuck with the implication that cruelty could possibly be morally right, nor do they want to accept the implication that the foundations of morality are arbitrary. So, a divine command theorist might avoid this problem of arbitrariness by opting for a different answer to Socrates’ question, and say that for any particular action that God commands, He commands it because it is morally right. By taking this route, the divine command theorist avoids having to accept that inflicting suffering on others for fun could be a morally right action. More generally, she avoids the arbitrariness that plagues any Divine Command Theory which includes the claim that an action is right solely because God commands it. However, two new problems now arise. If God commands a particular action because it is morally right, then ethics no longer depends on God in the way that Divine Command Theorists maintain. God is no longer the author of ethics, but rather a mere recognizer of right and wrong. As such, God no longer serves as the foundation of ethics. Moreover, it now seems that God has become subject to an external moral law, and is no longer sovereign. John Arthur (2005) puts the point this way: “If God approves kindness because it is a virtue and hates the Nazis because they were evil, then it seems that God discovers morality rather than inventing it” (20, emphasis added). God is no longer sovereign over the entire universe, but rather is subject to a moral law external to himself. The notion that God is subject to an external moral law is also a problem for theists who hold that in the great chain of being, God is at the top. Here, there is a moral law external to and higher than God, and this is a consequence that many divine command theorists would want to reject. Hence, the advocate of a Divine Command Theory of ethics faces a dilemma: morality either rests on arbitrary foundations, or God is not the source of ethics and is subject to an external moral law, both of which allegedly compromise his supreme moral and metaphysical status.