The first step in setting up an effective argument between characters is by giving each character a unique goal in mind. Creating an argument must be balanced between having the protagonist of the argument create a reasonable defense and having the antagonist of the argument have an understandable stance. Even if the antagonist's stance is something you may personally disagree with, being able to see where they are coming from and why they believe whatever it is they believe in is a necessity in creating an argument that is balanced with relatable characters. Having relatable or understandable characters is absolutely crucial in order for a story of conflict to succeed. If you don't have relatable or understandable characters, then the goals or ambitions of those characters are much harder to grasp. Having viewpoints that don't make sense can make the reader feel uninvested in the characters and characters that fail to give you reasons to care about them cannot create effective arguments.
