Unless there is a god providing an objective moral standard, there is no reason to prefer one moral claim over another.
If religious theists find that they aren't getting anywhere arguing that there can't be any moral standards without their god, they sometimes switch to arguing that without a god to provide an objective set of standards then there is no way to choose which is the best among the various human standards — why not accept Nazi standards, for example? It's a mistake to assume that only a set of objective, absolute standards can provide us with any guidance in moral matters, though.
If we assume that the only "correct" morality is one dependent upon the commands of some outside source, then of course we have to conclude that the absence of such a source eliminates any good reasons for being moral — but must we make such an assumption? I don't think so and I have yet to find any theists provide a good, compelling argument to change my mind.
I could assume instead that the only "correct" morality is one which enhances the good while minimizes suffering. Many religious theists might respond by asking what reason there is to assume that we should enhance the good while minimizing suffering, but here they would be relying upon the assumption that the only good reason to arrive at such a conclusion is if we are ordered to do so by an outside, superior force. You can't prove the validity of a position by assuming its validity as part of your argument.
That, however, is what religious theists typically do as a response to any other moral theory. They assume, without ever even trying to prove, that only their type of moral system can be adequate. This assumption should not and cannot be granted. When offering alternatives, like the idea that morality depends on enhancing the good and minimizing suffering, a substantive and serious counterargument must explain how the theistic alternative is superior.
It's quite common for a person defending the "divine command theory" of morality (in which morality is defined by what a deity commands, nothing more and nothing less) to ask how we can condemn the Nazis without relying upon a source of morality that is "independent" of humanity. After all, don't the Nazis have an equally sound claim that their moral system is "right" and valid?
Well, no, not necessarily. One might think so if we accepted the theist's premise that outside of God's opinion, all human opinions are completely equal. But what should this premise be granted? There are certainly contexts in which no one's opinion is any more "true" than the opinions of others, but that isn't obviously the case when it comes to morality.
We can make many sound arguments against the Nazis' moral system, one of which is the amount of human suffering it produces. If religious theists respond by asserting that we have no objective reasons to prefer that humans not suffer, then what they are saying is that they don't personally care if humans suffer unless ordered to by their god — and that's hardly a perspective that can recommend their moral position over anything else. If a religious theist really needs something more than the suffering of people to want to end that suffering, this doesn't speak well of their ability to empathize with other human beings.
The problem with making such an argument to a defender of divine command theory is that such people typically assume that only a perfectly independent source of moral standards is valid — hence, no argument from human experience will ever succeed with them. They are, in effect, impervious to any counter-arguments on this issue. They can't accept that the basis for your moral system is any superior to the basis of a Nazi moral system because neither basis creates absolute obligations and neither basis is absolute or objective. That your moral system leads to greater happiness and the Nazi moral system leads to greater suffering will be deemed irrelevant — an important fact to keep in mind.