Your eleven year old son, Matt, has come to you and told you that his older brother, Mike, who is thirteen, just called him an idiot. You expressly do not allow the boys to call each other names of any kind. You call for Mike and he flatly denies calling Matt an idiot. He said Matt disturbed his video game playing and all he said was, "Ugh!" This turns into a "you did too, I did not" argument between the brothers. You are feeling inclined to believe the younger sibling. Mike then gets mad at you and starts yelling at you. Yes, you should have got more information, but when Mike started yelling at you, it was all you could take. You gave Mike a spanking and took his video games for a week.
You find out later in the day the real truth. Mike was playing an especially difficult game and was almost ready to win when Matt barged in his room and disturbed him. Mike did get frustrated and, yes, all he did was yell out, "Ugh!" It seems Matt saw a good opportunity to cause some trouble for his brother.
How do you sort all of this out?