AND
Forums are a dictatorship, there is no other way to do it, but they need not be managed like a doctorship. Also, a benevolent dictatorship is NOT necessarily a bad thing. If you have a good group of moderators, then they should be able to discuss bad decisions in light of how to make better decisions, without hurting anyone’s feeling.
… prohibition against arguing moderation decisions.
I mostly disagree, but I understand why some boards prohibit this. Disagreement with moderator decisions is usually unproductive, but if people are complaining it may also indicate a problem with how the forum is managed. Mods can make mistakes, I certainly have. No one makes the right call 100% of the time.
If there is a complaint about a given moderator, let the other moderators handle it, if possible. If you don’t have other mods, you could always seek advice here.
Disagreements with moderators should usually be a private discussion.
Details about decisions regarding an individual should always be kept private, no matter how awful that person is. Exception for threats of violence.
If someone complains about my decision, my usual response is along the lines of “This is not an argument, this is because XXXX was unacceptable behavior.”
Attempts to justify that behavior are generally irrelevant and should be ignored, along with attempts to continue the argument. I do try to address requests for information, and consider the possibility that I could be wrong, or that the rules are clear enough. (What’s why the rules really need to be simple.)