The in-universe public stance on superheroes like Daredevil and The Avengers overall is not always the most flattering. Sometimes, the negative press is as unwarranted and unprompted as J. Jonah Jameson using every space of the Daily Bugle to slander someone who everyone else in New York would call their friendly neighborhood Spider-Man.
Some people just don't like the idea of an undocumented masked vigilante dishing out their own brand of justice on their own terms. But other times, it's perfectly reasonable why some crowds may protest the very idea of a superhero. Take Marvel's first Civil War arc as an example, specifically the Stamford Incident that incites the entire Superhuman Registration Act to begin with. It was a day in which 600 people, including 60 nearby children, lost their lives in an explosion caused by Nitro in the middle of a brawl with the New Warriors. There's a good reason Civil War turned Speedball into Penance. It's not hard to understand why such a huge bulk of the public immediately turns their backs on the general superhero population. Daredevil, though, is one particular hero who isn't so understanding of the public's scrutiny.
In New Avengers #19 by Brian Michael Bendis and Mike Deodato Jr, Daredevil finally speaks out about superhero criticism. In an inner monologue from Matt as he enters Avengers Mansion in front of an angry mob, he asserts that people shouldn't be protesting heroes who have put their necks on the line to actually make a difference in the world while so many others pass the buck. It's also worth noting that Luke Cage makes a counterpoint later in the same issue, telling Iron Fist not to confront the protestors because they want to live in a world where people are free to question them.
Moments like these highlight the complicated nature of being a superhero vigilante like Daredevil, someone who by definition works both outside of the law and with the law. It's a complicated dichotomy made further complicated by the execution. When superheroes do their job right, they save the world. When they make just one mistake, lives are either ruined or lost. Equally complicated is the evaluation of Daredevil's stance against the protestors. While it's understandable to see where he's coming from given how we as readers have seen heroes try their hardest to save people and readers know their efforts are genuine, those same heroes still have a responsibility to protect the public in their line of duty. By proxy, they need to be held accountable when their efforts fail. Ultimately, Luke Cage makes a great point as well because they as heroes work hard to protect the people so that those people have the right to freely have the choice of loving them or hating them. There's a reason Luke Cage makes such a compelling mayoral candidate in modern Marvel Comics.
Being a hero like Daredevil is a tough line of work and while the tactics of The Avengers may, at times, be questionable, they at least ensure that citizens live in a world that's free to question them at least.