The Euthyphro dilemma is a pretty well-worn workhorse in the philosophy of religion world – I won’t spend a ton of time explaining exactly what it is for that reason.
The standard reply is that neither of the horns is correct – something is good because God is good, and said things goodness is a reflection of His goodness. Here I want to leave the philosophy of religion world for a bit and head into a theological direction.
First, we have to have working definitions of good and evil. This is trickier than it sounds – but let’s say that good is that which allows for the flourishing of living things. I think that’s a decent definition. How about evil? Those of a more materialist bent are likely to not really think that there is such a thing as evil in the classical sense – but for the sake of argument, let’s say that evil, as classically stated (by, say, Augustine) is the absence of good. This has some interesting ramifications.
Classical Christian thought holds that creation is by nature good – evil is not itself a created thing but a kind of ontological shadow. It doesn’t have a positive existence of its own. Good, however, does – God created and said that it was good. Creation and created things are good. Evil is not a created thing.
So how does this apply to the Euthyphro problem? Well, perhaps this: something is good because God created it – by definition, if it’s a created thing, it is good. Is something good because God likes it or does God like it because it is good? Neither – something is good because it God’s creation.
I have a feeling this does less to answer the supposed dilemma than I hope – but at any rate, this is a more theologically-minded kind-of answer to the issue at hand,