How do you console a person who misunderstood you?

Give them time to cool off. Apologize and state they misunderstood. If they want to understand, they will ask you to explain. If they care about you more than they need to understand or hold onto a disagreement, they will likely let it drop. You could let it drop for the same reasons, also. I doubt it matters much, in the long run. It is difficult to recall what we ate for breakfast yesterday, let alone last week. The momentary disharmony will pass.