The question, then, is not whether to argue, but how. Here are some suggestions:
Start positively
Ensure your opening comment contains something (sincerely) affirming about your partner. According to Gottman, this is important not only when you disagree, but in everyday conversations as well.
For relationships truly to thrive, he recommends that comments indicating respect and showing gratitude for your partner's positive qualities should outnumber negative comments by a ratio of five to one.
Acknowledge your role in maintaining the discord and creating your own distress
No one can make another person feel upset: it's entirely up to each of us how we react to what happens. Furthermore, chronic disputes are almost never attributable to the actions of only one person.
Think about and acknowledge your role in maintaining your distress and the ongoing differences between you.
Keep to the issues
Focus on the issue of disagreement rather than personal qualities, and avoid descending to name-calling or insulting. Whenever you feel unclear about something your partner says, ask for clarification – and listen.
Take turns
Avoid interrupting. If you feel unable to control yourself, ask for a break – 20 to 30 minutes is enough; longer is fine if you think it necessary. Take a walk, practice yoga or deep breathing – anything that releases your tension. If this happens often, consider discussing sensitive issues in a public place such as a park or outdoor restaurant. We're less likely to allow emotion to swamp us if we're in view of others.
Prepare ahead
John Platt at the University of Chicago writes the way to find the best solution to a problem isn't simply to defend your solution, but to think through all possible approaches and determine why none of them works as well as yours. This more scientific approach is, by the way, likely to help you refine and improve your own solution.
Expect to compromise
No one has explained this more clearly than French essayist and moralist Joseph Joubert, when he wrote, "the aim of argument, or of discussion, should not be victory, but progress".