What do you say when someone mad at you but you can't say I am sorry?

You can say " I am sorry you feel as you do". The only way to avoid an argument is to not be a part of it. State the facts as you understand them and ask if that is the way that they understand them to be. If there is a values difference then one of you must change or agree to disagree but then only time will modify the difference in values. Sometimes, the facts are not what they seem and then it is easy. Facts and values are items to focus on.