Sometimes, we are engaged in a war of words, or some differences, or a fight with someone. This is our dirty linen. These are tense moments for us. Our mind is unsettled. We are filled with rage, and anger at the other person. We feel we want to expose the other person. We want the whole world to know his wrongfulness. We decide to wash our dirty linen in public.
When you do so, you risk yourself being maligned in public. The other person won't take your public insult lying down. Are you ready to be insulted in public?
Also, whatever your differences today, may get solved tomorrow. Maintaining a low, private profile of your fight is better.
Lastly, if you believe in karma, have faith that if you are right, then karmic justice will be done and the other person will be punished in some way or the other. By throwing a dirt full of insult in public and taking justice in your own hands does not help.
Don't wash your dirty linen in public.