Sometimes you don't have to argue. Sometimes silence is the best answer. Letting go may be the best thing to do when confronted with a person or situation that will not change. When annoyed, confused or irritated, sometimes we are better served by waiting rather than reacting. Living sober means acting upon situations not reacting to them.
The Big Book teaches us to pause when agitated, that self restraint is the first step to acting upon a situation. Remember that we control ourselves, not them.