What is it about fighting in dialogue that makes a writer drag out every last detail? For instance, a fight between John and Mary might go like this:
M: How could you?
J: It just happened.
M: But we've been married for thirteen years, John!
J: I know that, Mary. It just happened!
M: How? We have two children together, we've been happy!
J: I can't take it back, Mary. I'm so sorry. Can you ever forgive me?
M: Remember when you proposed, you said you would never, ever hurt me?
M: I guess you just broke that promise.
Telling, telling, telling. All I see is information here, not subtle in the least! Fighting between characters is one of the easiest telling-traps to fall into. The most logical reason for that is real-life fights tend to go this way. We lay out our issues to one another, listing all the reasons why the other peson in the fight screwed up, and all the reasons that they shouldn't have done so.
Sure, it's real, it happens, and most of us could probably recite our greatest fights word for word...but it's boring, folks, and - to put it simply - it's easy.
Think of the movie The Bourne Identity. Jason Bourne actually uses a magazine to fend from a guy with a knife. Knife vs. Magazine. Now that's a fight I was interested in! Bourne didn't stomp around the kitchen railing at the guy like this:
Bourne: How dare you come at me with a knife! You have no business being here!
Knife-Guy: But I've been sent to kill you! With this knife!
Bourne: Why? Why are you doing this? Can't you just tell me who I am? I'm lost!
Knife-Guy: No, I can't do that. Now let me attack you.
Bourne: No! I won't let you!
A married couple might fight like this, but let's keep our characters in the freshwater-pond, instead of a dull, gooey swamp. Here's an exercise:
The next time your characters are fighting, try to write it without dialogue - see what they do. What actions would either character use to express their anger? What would be the ultimate act that one might perform to show the other that they're mad?
If you want a little dialogue, try writing the fight with no information. Instead of listing the reasons why your characters are in the fight, think of things they might say to skirt around the fact that they're not happy with one another - maybe a normal conversation amid actions that express something more rancorous is going on. For example, a husband and wife mid-fight might have breakfast together, talking about the husband's day at work, but meanwhile, the husband is slapping jelly on his toast as though he were hitting a person, and the wife is digging at grit in the pan with her spatula so hard that the handle breaks off.
Focus on any fight at all and see how you wrote it. Are the characters repeating already-known information back to one another? Are they doing things during the fight, or just standing around like dolls? Could they be doing something that might be a better way to show that they're having a fight?