The Euthyphro Dilemma

The most common argument against divine command theory is the Euthyphro dilemma. The argument gets its name from Plato’s Euthyphro dialogue, which contains the inspiration for it. 

The Euthyphro dilemma is introduced with the question, " Does God command the good because it is good, or is it good because it is commanded by God? "  

Each of the two possibilities identified in this question are widely agreed to present intractable problems for divine command theory.

Suppose that the divine command theorist takes the first horn of the dilemma, asserting that God commands the good because it is good. 
 

If God commands the good because it is good, then he bases his decision what to command on what is already morally good.

Moral goodness, then, must exist before God issues any commands, otherwise he wouldn’t command anything. 

If moral goodness exists before God issues any commands, though, then moral goodness is independent of God’s commands; God’s commands aren’t the source of morality, but merely a source of information about morality. 

Morality itself is not based in divine commands. 

Suppose, then, that the divine commands theorist takes the second horn of the dilemma, asserting that the good is good because it is commanded by God. 

On this view, nothing is good until God commands it.

This, though, raises a problem too: if nothing is good until God commands it, then what God commands is completely morally arbitrary; God has no moral reason for commanding as he does; morally speaking, he could just as well have commanded anything else. 

This problem is exacerbated when we consider that God, being omnipotent, could have commanded anything at all.

He could, for example, have commanded polygamy, slavery, and the killing of the over-50s.

If divine command theory is true, then had he done so then these things would be morally good. That doesn’t seem right, though; even if God had commanded these things they would still be morally bad. Divine command theory, then, must be false.

http://moralphilosophy.info/normative-ethics/deontology/divine-command-theory/the-euthyphro-dilemma/