Euthyphro’s dilemma is found in Plato’s works. It’s designed to confuse polytheists, but modern atheists also use it to oppose the Christian view of morality. It states, in the original “Is the pious loved by the gods because it is pious, or is it pious because it is loved by the gods?” When used against Christianity, it is stated as in today’s image (ignore the Bible verse for now).
If God calls good good because it is good, that necessitates the existence of a moral standard higher than God, to which even He is bound. Therefore, God is not sovereign. If the latter is true, and good is good because God says it is good, then God cannot claim to be perfect because the standard can be shifted at any point.
There is, of course, a third option. It is significant that the original dilemma was posed against polytheism, not monotheism. Polytheists believe in multiple, independent, often finite gods. They are often capricious, and are merely part of the creation. By contrast, God is completely sovereign and self existent. The Bible describes Him as the first and the last. In other words, but for God, nothing would exist. That includes this world, which the Bible explicitly tells us He made. In other words, He is the designer, and so He both gets to decide what the world should be like, and judge whether it works that way.
In my original image, I used the example of a watch made by a watch maker. In the Bible, I’m aware of at least two areas where God compares Himself to a potter making pottery. Another example would be an artist judging their own art. When it comes to creative arts, only one opinion matters: the opinion of the creator.
The Bible also rejects the idea of a capricious God. He doesn’t change on a whim, He has a plan in His mind, and He doesn’t change that plan. God isn’t even bound by our concept of time. Time is yet another of His creations. This means He cannot be surprised. He can’t learn anything new, He can’t be surprised by new information or unexpected events. Therefore, He can never change. He doesn’t need to. His character has been established forever.
Therefore, Euthyphro’s dilemma does not apply to God. It’s not that God answers to a higher standard, nor is it that He is capricious. Rather, God has a very specific plan in His mind for everything He creates. When that design works as it should, that is good. When it doesn’t, that is evil.
Let’s take the very specific example of murder. Is murder evil because God says, or does God say it’s evil because it’s evil? Both. God says murder is wrong because life is good. Life is good because God designed it to be lived. God is both the standard and the judge of that standard. There is no dilemma here.