Unsurprisingly, the authorities denounce vigilantism. Yet vigilantes are very popular in fiction. More realistic examples include the Dirty Harry series and Person of Interest.
Then you have the whole genre of superhero vigilantes, viz. Superman, Spiderman, Batman, Green Arrow–plus video game characters like Max Payne.
The usual context of fictional vigilantes is when the authorities let crime spiral out of control. Indeed, the authorities are often in cahoots with the criminal class. They get kickbacks for looking the other way.
The authorities resent vigilantes because it make them look bad. It shines a light on their incompetence or corruption. The effectiveness of fictional vigilantes is a constant embarrassment to the ineffectual authorities.
There's a popular audience for this character because it has real-world parallels. Big city mayors or US presidents who don't do their job. Who don't protect the citizenry.
Indeed, we have situations where the authorities perversely protect the bad guys from the good guys. Just recently, in the wake of another jihadist attack (in San Bernadino), the Attorney General vowed to crack down, not on domestic jihadism, but "anti-Muslim rhetoric."
I think the popular audience for fictional avengers also reflects an instinctive yearning for eschatological justice. So many crooks elude justice, including heinous criminals. And it never ends. It's like a secularized Second Coming.