Don't break up. Fix the problem. Start the romance again. Go on dates again. Work on winning each other over again. This is why there are so many failed relationships. If you love each other and are best friends then breaking up is not the answer. Because you are NEVER going to find that again. You need to realize one little thing is about to ruin probably the rest of your life because you both where too stubborn to say sorry and move on. And now I have to avoid talking to someone for months again because it got too toxic for me to even breathe. I've actually been in the hospital as of recent more frequently and the awkwardness of seeing him makes me realize it's just not meant to be. But I hope whoever is reading this realizes the most important thing about a relationship is, ATTENTION, AND COMMUNICATION. When those two factors are gone, it messes up the whole relationship. Take a deep breathe, hug your partner, realize being angry forever isn't going to change anything. Get back to how it was before the fight, and realize you rather have a forever than a month.
But hey, I hope this saves some people's relationship.