Arguing with your stakeholders is never good.
The basis of an argument is to defend your position while defeating the other person's in the process. It's easy to suggest using active listening to understand the other person's viewpoint, but this advice overlooks the inevitable build up of emotions inherent in any argument.
Asking the help of a third party to mediate an argument with a stakeholder can be very useful. First, the presence of an observer helps contain excessive emotions. Secondly, a third-party observer can bring fresh insights to help move the argument to a constructive discussion and, ultimately, a solution.
Transitioning from a sides-based argument to an "us"-based solution does not require the third-party observer to necessarily solve the problem. Rather, the mediator should help those arguing to develop a solution.
An ancient legend demonstrates this concept beautifully:
A farmer died and left his herd of 17 camels to his three sons. In his will, he left half of the camels to his eldest son, one third of the camels to the second son and one ninth of the camels to his youngest son.
The three brothers were having great difficulty working out a fair way of implementing their father's will and could not agree on who would have more and who would have less than the amount willed. Before their relationship became too stained, the brothers went to visit a wise old woman who lived in their village to seek advice.
She told them she could not solve their problem but would give them her only camel if it would help.
The brothers thanked her and took the camel back with them. With a herd of 18 the problem simply disappeared; the first brother took 9 camels, the second six and the youngest two.
But, 9 + 6 + 2 = 17, so they gave the spare camel back to the wise old lady with their thanks.
The point of the story, from a project management perspective, is that belaboring arguments with stakeholders will only succeed in delaying the project. For the sake of keeping the project within the triple constraints, it's best to resolve arguments promptly and for the good of the project.
In your projects, how have you handled arguments? Do you seek help before positions become entrenched?