The 'Evil God Challenge' (EGC) is an argument that every argument for a good God has an equally plausible counterpart argument for an evil God; the conclusion is typically that both are equally absurd, or that neither should be accepted. For some reason I cannot fathom, it seems to be enjoying a bit of a surge in popularity, which I find extremely irritating, because I think it is one of the most extraordinarily stupid arguments I've come across, to the extent that I regard taking it seriously as a sign of intellectual incompetence. There are many reasons why it is a ridiculous argument; here are just a few.
(1) The EGC does not establish what it is supposed to be establishing. It seems to pass by a great many of the people who propose the EGC, but if I have a claim (e.g., the world is good) that implies X, and the opposing claim (e.g., the world is not good) also implies X, these do not magically cancel out; what they establish is that, asssuming the propositions are meaningful, X is true no matter what, i.e., that it is a necessary truth. If I have a plausible valid argument, using terms like 'good', for "God exists and God is good", and I have an equally plausible valid argument, switching out the good-valenced terms for the bad-valenced terms, for "God exists and God is evil", what is very noticeable is that I can conclude "God exists" from both. If the premises are meaningful at all, and if good and evil are actually relevant to the question at all, then the most natural conclusion is that "God exists" is a serious candidate for a necessary truth. If the arguments are plausible and equally plausible they do not 'cancel out' in a way that touches the conclusion "God exists". This is part of how arguments from parity work; if something seems to follow equally from opposites, that makes it more probably true, not less.
Thus the only way the EGC could have any purchase against theism in general is if we knew that all the arguments for a good God were implausible and probably wrong. But nothing about the EGC could possibly establish this, and if you already had an argument that all the arguments for a good God were probably wrong, the EGC couldn't actually add anything to it except to rule out arguments for an evil God, which almost no one accepts anyway.
(2) Proponents of the EGC consistently show that they don't understand the difference between 'parody argument' and 'parity argument'. The EGC is an argument from parity. That is to say, it claims that if you accept such-and-such argument, you should equally accept such-and-such argument, because the grounds or reasons for accepting them are not different in a way that matter. (Parity arguments are related to, but weaker than, a fortiori arguments, which claim that if you accept one argument, you have even more reason to accept another.) One way you can run an argument from parity is to create appropriate parody arguments. A parody argument is where you take an argument and substitute other things for its terms to get absurd results. However, most parody arguments are completely useless for parity arguments, and even when you have a parody argument that might be suitable, you have to use it in the right way to create parity. The reason is very obvious -- you can make parody argument for any argument, just by substituting terms.
There is literally no person on the planet more painfully stupid than the person who thinks that you can object to an argument just by taking it, replacing its terms, and getting an absurd or silly result. If you do this, congratulations; you have just discovered that the argument has logical structure. Arguments have a logical structure that they share with lots of other arguments; they can share it with other arguments because the logical structure is detachable from the content of the argument. No argument can be refuted by merely showing that it has a logical structure. Just because you can take an argument that has 'good' in it, then substitute 'evil' for 'good', and get another argument doesn't tell us anything at all about how to evaluate either argument.
In order for your parody argument to be relevant to an argument from parity, you have to show that there would be more-or-less equal reason to accept the parody. This is a completely separate step. Over and over you find proponents of EGC spending an awful lot of time making parody arguments and, at best, vaguely handwaving the whole question of whether the parody is suitable for parity. This is a red flag; they are skipping or rushing through the hard step that actually does the real work. And it brings us to the third point.
(3) On no major ethical approach do good and evil have the symmetry required to get the equality. Unsurprisingly, once you use your brain to think about it, almost no form of ethics takes good and evil to be symmetrical so that you can simply interchange their terms in arguments without radically changing how you would asses the arguments. On most theories of good and evil, good and evil are not symmetrical with regard to power, intelligence, or results. This is why various forms of ethics don't have a problem with distingishing themselves from their equal and opposites. Utilitarians don't have to puzzle over why morality is based on maximizing happiness rather than maximizing suffering. Good is desirable, evil is undesirable. Kantians don't have to puzzle over why they should accept morality is a kind of conformity to reason rather than a kind of self-contradicting irrationality. Good is consistent, evil is inconsistent. Aristotelians don't have to puzzle over why our nature is completed by a totality of goods rather than a totality of evils. Good is fulfilling, evil is unfulfilling. In none of these cases are the two symmetrical and interchangeable; we can distinguish good and evil perfectly well, and know that if you switch the terms in any argument to which the meaning of the terms is genuinely relevant, it is extremely unlikely that you would get equally plausible arguments.
And in fact, if the EGC were any kind of argument worth taking seriously, it would do far more damage to ethics than to natural theology, because having the kind of symmetry that the EGC requires would mean that many ethical arguments would also have a problem, because their uses of 'good' and 'evil' are linkable to 'good' and 'evil' in the theological case, through positions like theological utilitarianism, Kantian philosophy of religion, etc. If you are a theistic Kantian, for instance, you postulate that God exists as willing the moral law, to solve a problem with respect to living a moral life. It is literally impossible to do this on Kantian principles and coherently postulate an evil God. If you try to insist to a theistic Kantian that there is an equally plausible argument for an evil God, you are saying that Kantian ethics is no more plausible than its direct opposite, which obviously a Kantian has no reason whatsoever to accept. (And indeed shouldn't, because even non-Kantians can see that Kantianism is more plausible than its polar opposite.) Things are a little more complicated for utilitarianism or Aristotelianism, because they have slightly more complicated accounts, but you get similar results for similar reasons. The EGC only works if ethical ways of using 'good' and 'evil' are no more plausible than their opposites.
This is related to another problem for the EGC.
(4) On neither of the two most plausible accounts of the relation between good and evil (the account on which they are related as positive and privative and the account on which they are related as pleasing and displeasing) is the symmetry required by the EGC possible. These points have been discussed at length by others, and are obvious in themeselves, so I won't develop them here.
Honestly, I could go on. For instance, when proponents of the EGC actually get off their backsides and try to show that every argument for a good God has an equal and opposite counterpart argument for a bad God, they end up repeatedly mangling the former, or failing to address obvious problems with the latter that arise specifically from their appeal to badness. This is tedious work, but of course, even one argument for a good God having no equally plausible counterpart for an evil God breaks the EGC. Proponents of the EGC make bold claims, but they repeatedly show that they cannot deliver the goods when it comes to details. It's just a stupid argument all around.
