I am expanding and hopefully improving on a previous argument against divine command theory, given here. According to divine command theory, the wrongness of an action is metaphysically identical to the actions being contrary to the commands of (a loving) God. My objection takes the form of a dilemma: Either God can issue commands to people knowing they will have rational doubts about its authenticity, or he cannot.
If he can, then we have a strong counter example to divine command theory. Surely having rational doubts about the authenticity of a command nullifies any obligation to obey it. For example, if you received a note from the government that lacked any official markings and appeared to be inauthentic, then you can't be expected to meet their demands. And if the government didn't even put any effort into presenting the command to you in such a way that you would recognize its authenticity, then it seems absurd to think you are under any obligation to do as they require of you. With this, it follows that it would be possible for God to issue commands without generating any obligation for the recipient to obey. And since facts about identity are non-contingent, divine command theory must be false.
If he cannot, then divine command theorists face a similar challenge that's almost as bad. For if God has issued someone a command, then as long as they are rational they will recognize that the command comes from God and not anyone else. But if a rational person is aware that God has issued them a command, then they are aware that God exists. And so, if a rational person has received a command from God (i.e. if they have a moral obligation), then they are aware that God exists. But there are many rational non-believers who do not believe and are not aware that God exists. And so there are an uncomfortably large number of people who must have never been issued any commands by God.
And so divine command theorists are impaled on either of the two horns of this dilemma: either they're confronted with a compelling counter-example to divine command theory, or they must admit there are a great many people for whom every action—no matter how monstrous—is morally permissible.