Not all arguments are designed to change a person's mind. Some are designed to (change one's behavior). A lot of arugments/fights between couples have to do with setting boundaries, demanding respect, consideration or empathy. If a person knows certain things upsets their mate they will try and avoid doing or saying those things. (Assuming they love them and want them to be happy).
Fights involve ego and demand a "winner" and "loser". It becomes all about (You & Me) rather than an (Us & We). Some people don't quit fighting until they force the other person to apologize or give up. Their ego requires them to "win" in order to feel good. There are times when you have to agree to disagree. Not every issue is a "deal breaker" nor should it rise to the level of World War III. As one author put it, "Don't Sweat the Small Stuff". If a couple fights all of the time they are probably not right for each other.