Everyone knows when you see two dogs tearing into each other, the last thing you should do is try to get between them. What some don't realise is that the same can be true of people, too.
This trope is when two characters in the middle of a bitter argument make up their differences over a common love of abusing someone else — usually the first person who intervenes to get them to make up. They'll tend to start out with grudging Dumbass Has a Point and Actually Pretty Funny's, before really warming to the tag-team beatdown.
Can cross over with Truth-Telling Session.
Subtrope of No Good Deed Goes Unpunished, and related to Stop Helping Me!. Inversion of Apple of Discord, when a third party makes two allies start arguing - this is about making two arguers temporarily join forces against the intruder. Compare/contrast Enemy Mine, when two mortal enemies join forces to defeat a mutual threat, and Genghis Gambit (where the mediator deliberately invokes this).
As Revy and Roberta are beating the nine hells out of each other in Black Lagoon, Rock gets the bright idea to try to get them to talk about their problems. Being as both of them are in full-on violent mode, the response from the two is unsurprising:
Revy and Roberta: (simultaneously) STAY THE FUCK OUT OF THIS!
Ranma ˝: When Gosunkugi gets ahold of paper dolls capable of controlling anyone he wishes, he tries to use this opportunity to win Akane's heart. Unfortunately, after he test-drives a few of his dolls on Ranma to see if they actually work, Ranma's suspicions are raised to the point where he openly confronts him about it. Akane immediately rushes to Gosunkugi's defence and our two opposing sides begin to bicker.
Ranma: How come you're bein' so stupid, stupid?!
Akane: Speaking of stupid, look in a mirror!
Gosunkugi: Um, Akane? Ranma? Please calm down. I haven't put the doll on, so can you not fight until I-
This is a pretty common fate for anyone who steps in between Ryoko and Ayeka. The biggest one comes towards Tsunami, who finds her explanation about herself and Sasami interrupted because the two are more worried that Tsunami is gonna be Sasami in the future and when she tries to get their attention, they both tell her to shut up!
In the Robert Asprin book The Sweet Myth-tery of Life, Guido describes this as an inevitable result of getting involved in a domestic dispute.
As previously shown by Skeeve in Hit or Myth, when he got the reluctantly married king and queen to get along by telling off both of them. (And wisely brought bodyguards when he did it.)
Very deliberately invoked by Saki in "Excepting Mrs. Pentherby".
In Dresden Files, Harry tries to defuse what's about to go down between Ebenezer McCoy and Jaren Kincaid. He ends up with a gun pointed at his face and his spine.
Discussed and defied by the Feegles in I Shall Wear Midnight - "Any man who interferes with the arguin' of women is gonnae find himself with both of them jumpin' up and doon on him in a matter of seconds".
In Black Books, Bernard and Mannie take time out from an argument to insult Fran, and end up resolving their own differences in the process. Until Fran leaves the room, at which point things go back to normal.
JD: And just like that all the hatred they had for each other was instantly directed at me.
In the Xena: Warrior Princess episode "Been There, Done That", Joxer attempts to invoke this trope in order to stop the feuding families. He gets a couple dozen arrows to his face for his trouble (but again, this being a "Groundhog Day" Loop, he gets better).
Played with on Frasier; Frasier sits Roz and Julia down in the cafe to try to get them to make nice, and when they find common ground insulting him, he graciously leaves them to it. The moment he's gone, though, they both get up to leave, and are bickering again before they reach the door.
This trope, along with The Masochism Tango, is the entire point of the Edward Albee play Who's Afraid Of Virginia Woolf. George and Martha attack each other at every turn, but take more delight in ganging up to tear apart the innocent young couple they invite round for drinks, (lots and lotsof drinks). It's heavily implied they do this all the time to keep them from killing each other.
On The Simpsons when Marge went after Itchy and Scratchy, the series staff did an episode where a squirrel character based on Marge tries to stop a fight, but the duo decides to knock her head off instead. Given that the only other time they've worked together against someone else was an old wartime special where they beat up Hitler...
Zig Zagged in the My Little Pony: Friendship Is Magic episode "Over A Barrel": Pinkie Pie tries to settle tensions between the settlers and the buffalo with a song-and-dance number. They briefly agree... that it's the worst song they've ever heard... and then go back to fighting. Later, just as the buffalo are about to give up their stampede, she reprises it... and they decide to go through with the stampede as a result.
In the SpongeBob SquarePants episode "The Other Patty", Mr. Krabs and Plankton grudgingly team up to try and steal a new competitor's secret formula. Throughout the episode, the two spend their time disagreeing and bickering with each other. It's eventually revealed that SpongeBob started the competing restaurant to help Krabs and Plankton's friendship. The two respond by chasing after him, with intent to beat him up.
Witness any police intervention in a domestic argument. (Or anybody else's, of course, but the police are the only ones professionally obliged to stick their heads over the parapet.) What they tend to really hate about such jobs is that even when one partner is clearly being abused, they'll often firmly take their abuser's side.
This can happen on many internet forums. Trying to end a Flame War between two or even more users will result in them to take out their frustration on you with heaping insults. Considering that it's the internet, this is no surprise at all.