To stop an argument, first stop arguing. Then, speak with fragrance of resolution, not the stink of confrontation. Arguments stem from doubt. They are the usage of anger to force verification of a value that you yourself do not believe. Convincing another through an argument is actually striving to convince yourself.
Working the inside is more effective. Achieve inner approval, so that you will no longer need it from the outside.
Experience your existence and remove the arguments that deny it, there is nothing to justify or verify, there is no need for a witness to validate your existence.
This is a state of grace and of true compassion. It is peace of mind and fulfillment of the heart.