How to politely explain editor is wrong We have a paper that is a second round R&amp;R at a Journal that is a cognate field which is less technical than ours. The editor has been extremely conscientious and supportive through the process, but has made several suggestion that reveal he doesn’t really understand some of the deeper methodological details of our approach. In particular they are concerned that X could be playing a role but this is definitely not the case. 

I don’t want to respond saying X can’t explain our results because textbooks prove otherwise.  We could probably handle this but this is the second round in which they have suggested X is an issue/explanation, despite us gently explaining in our first round response and adding a footnote explaining why X was not an issue. So we need to find a better way of persuading him that this isn’t an issue. 

In particular, I am interested in solutions that avoid the need to explicitly contradict him.
I think you just lay out the facts as you see them, pointing to supporting evidence as necessary. If the editor can't be convinced then how you say things isn't going to matter much. Let the facts speak for themselves. Point up the flaws in X as applied to your work. And if you need to reference textbooks, do so, even citing page numbers. 

You may lose the battle, but it may not be winnable at this journal. If the reviewer is wrong, but is someone trusted by the editor you have a losing situation. If you sense that then withdraw politely and go to another journal.