Hands Off My Fluffy

Our heroes face a bloodthirsty-looking monster that is six feet tall with a thousand pointy teeth! Oh, and it is attacking that cute girl. Attack!

Wait, why is the girl throwing rocks at our heroes?

It turns out that the girl kept the monster as a pet, and they were playing. Bonus point if the monster is, in fact, harmless.

This is what happens when What Measure Is a Non-Cute? and What the Hell, Hero? intersect.

The title comes from Fluffy the Terrible, the creature whom our protagonists are foolishly trying to get rid of.

Not to be confused with,....er...nevermind. Cue the choruses of "I thought it meant...", jokes!

Examples of Hands Off My Fluffy include:

Anime and Manga

Fullmetal Alchemist had a variation on this. Scar, the neighborhood serial killer, comes out to violently attack our heroes. Mei Chan attacks the Elrics when they try for a finishing blow, and runs off with an injured Scar.
In El-Hazard: The Magnificent World, Fujisawa-sensei "rescues" Miz from her monstrous manservant. He turned out to be safe, and Miz decided to go with it since it might result in Rescue Romance.
One of the first stories in Gintama has the daughter of an alien diplomat trying to rescue her unknown massive alien being. Gin cuts it up.
- Inverted later when Shinpachi thinks Kagura's new alien giant dog is playing with her, Gin informs him that the dog's attacking her and she's too powerful to notice.
Bleach introduces Nel in this fashion. Ichigo "rescues" her from a group of arrancar who turn out to be her friends.
- Incidentally, Nel is playing "endless tag" with her friends, and since "Nel is a masochist" (and a loli with her arrancar mask covered), their "game" looked an awful lot like three hollows chasing a sobbing little girl. Actually, that's exactly what it was.
In Digimon Tamers, this probably would have happened with Antylamon (the last Deva yet to be revealed) had Shiuchon not been given her Digivice before Takato and Jenrya could think of attacking. And Zhuqiaomon reverts him to Lopmon shortly afterwards, confirming (see Redemption Demotion) his Heel Face Turn.

Fan Works

Simultaneously invoked and inverted to amusing effect in Doghead Thirteen's Harry Potter fic, Enter the Dragon. Hyperactive!Dragon!Harry -- who's about 10 or so -- knows that dragons in stories get treasure and maidens. Too innocent to know better, he decides maidens are another, better form of treasure, and when one is finally offered to him -- Suze, daughter of Bane, from the centaurs of the Forbidden Forest -- he treats her very well indeed. And once she realizes that she's dealing with a child and not a ravening monster, she comes to adore him as a kind of little brother, and she slaps her father when he tries to attack Harry not long afterward.

Literature

This is featured multiple times in A Series of Unfortunate Events, both the movie and the books, with the Incredibly Deadly Viper—most notably when it "attacks" Sunny.
While Hagrid from Harry Potter is far from a cute young girl, his attachment to his exotic pets does fit. He names the three-headed dog Fluffy, he is upset when he has to send his baby dragon Norbert away, and he cries buckets when the giant spider (Acromantula) Aragog dies. He was expelled from Hogwarts for keeping dangerous critters as pets, including Aragog. Harry and Ron are often at a loss to understand him, though the Trio does recognize why he is upset over the scheduled execution of an innocent hippogriff.
- Hagrid himself is a version of this. Giant hairy scary guy who can bend rifle barrels with one hand comes knocking down the door? If the Dursley's were proper foster parents instead of assholes who didn't give a crap about Harry, they'd probably freak out when Hagrid approached Harry. And when Hagrid is outed as a half-giant, many wizarding parents are terrified that he's a vicious monster who'll hurt their kids, when he's actually one of the gentlest, sweetest characters in the entire series.
Almost happens in Earth's Children, when the lion Ayla raised from a cub comes back to visit her in the human village she has moved to. She manages to stop the hunters before they harm the lion.
The Enchanted Forest Chronicles contain multiple examples, especially in the first book, Dealing With Dragons. A princess, Cimorene, runs away and volunteers to be the captive of a dragon; she then spends her time trying to stop knights from fighting the dragon because she doesn't want them to rescue her.
In Something MYTH Inc., Gleep the baby dragon gets accidentally shot because a trigger-happy bowman thinks he's attacking when he just wants to play.
In Keeper of the Isis Light, the main character's gigantic pet is killed when it tries to engage a human in a game of fetch.
Mercedes Lackey's One Good Knight provides a borderline example. While the Dragon in question did ravage The Kingdom of Arcadia until provided with weekly virgin sacrifices, it turns out that it was operating under a Tradition-reenforced geas and took pains to avoid harming any thinking creature... including the impromptu phalanx of dragonbait *ahem* maidens that confronted the heroes when they tracked said beast to it's lair.
In Tanith Lee's The Dragon Hoard, early, while Jasleth is looking for a quest to join or a monster to slay, he comes across a prince tussling with a two-headed monster, but it turns out that the monster is the prince's pet, they were just playing, and neither appreciates Jasleth's offer of assistance.

Live Action TV

In the Doctor Who story The Rescue, the relationship between 20th century companion Barbara and 25th century companion Vicki starts off badly when Barbara "rescues" Vicki from being "attacked" by a 6-foot-long, tooth-baring (vegetarian) lobster-monster... by shooting it in the face with a flare gun.
A sketch on The Dave Allen Show had a slavering werewolf doing a typical horror movie stalk of a Distressed Damsel. When he finally cornered her, she holds up a leash and calls "Walkies!" while the werewolf bounds about like an excited puppy.
Happened with Angel in one episode. A pregnant woman was being followed by an armor-plated demon. Angel kills the demon but discovers that it was protecting her from other demons.
- A nice Double Subversion: Cordelia, trapped in a unknown dimension ends up being chased by a vicious beast who catches her and... licks her face?. Whew. Then the pet's owner showed up, congratulated the "dog" and chained Cordelia. Unfortunately, it turns out that while the beast was a pet, it was a hound hunting... humans.

Newspaper Comics

Some something (probably a comic strip)^{[please verify]} had two heroes trekking through a jungle and encountering a group of monkeys molesting some naked women. The heroes shoot the monkeys, the women cry (they were married or something) and the adventurers quietly creep away.
- Voltaire's Candide (published in 1759) had this in the story. The heroes "rescue" some women running from apes, who turn out to be their husbands.

Video Games

The June 2009 trailer for Team Ico's The Last Guardian sets this up.
Subverted in Shadow Hearts: Covenant. A giant cat attacks you at one point. This is Lucia and Carla's pet, Andre... but they don't mind you beating up their cat because, frankly, the cat didn't have a reason to hurt you and you were just defending yourself.
H-game Nocturnal Illusion. To wit: A girl named Yuka lives in a shrine on the mansion grounds where the game takes place, and her story arc begins with your character reacting in horror as she's having sex with what looks like a demon. Willingly. It only get more disturbing when you find out the demon used to be human being, namely her Ill Boy brother who she fell in love with and who became a demon instead of dying. Oddly enough, it was the love between them that let him retain enough humanity she not only became his Morality Chain (albeit only to the point she is safe from harm), but the reason they fell for each other was because he was ostracized by his family for his disease and she was the only one who watched him during his final days to the point he grew to love her because she was literally all he had, and she fell for him because he was so devoted to her. However, he's still a demon and the whole Brother-Sister Incest thing is just chock full of Squick, so you have to put the demon out of its misery and help Yuka readjust to a normal life afterwards.
Becomes a major character-driving plot point for one villain in Tales of the Abyss, where the monster in question was the adoptive mother of the little girl, who naturally spends the game trying to avenge her giant carnivorous mommy.

Western Animation

In the Pilot Movie of Foster's Home for Imaginary Friends, Eduardo saves Mac (whom he had followed around, since he's too shy to introduce himself) from an Extremesaur. Bloo thinks Ed is attacking Mac and jumps him. Eduardo would have easily dispatched Bloo if he wasn't such a scaredy-cat...
An episode of Avatar: The Last Airbender had Aang trying to find a crazy king's lost pet Flopsie as one of three deadly challanges. He thinks it's the cute and cuddly rabbit being chased by the 7 foot tall gorilla-goat thing. He eventually figures out the trick and even learns an Aesop about it (after the climatic fight with the king, of course).