On Saturday, Ismaaiyl Brinsley shot a former girlfriend in Baltimore. Hours later, in Brooklyn, New York, he ambushed and killed two police officers in their car and then killed himself. New York Mayor Bill de Blasio described the murders as “execution-style.” Police don’t have a motive for the shootings, but Brinsley had a long criminal record—he was arrested for robbery charges in Ohio in 2009 and served two years in prison for felony gun possession in Georgia—and had made anti-police messages on Instagram the day of the shooting.

These deaths come at a terrible time for New York City. Between the killing of Eric Garner in Staten Island and the shooting of Akai Gurley in Brooklyn, many residents are wary of the police. And their protests against police brutality have fueled a counter-movement from cops and their supporters, who see criticism as hostile and “anti-police,” and who have scorned officials who sympathize with the protesters. “Police officers feel like they are being thrown under the bus,” said Patrick Lynch, president of the Patrolmen’s Benevolent Association, after de Blasio spoke about Garner in the context of his son, who is black. “Is my child safe, and not just from some of the painful realities of crime and violence in some of our neighborhoods,” said de Blasio, “but safe from the very people they want to have faith in as their protectors? That’s the reality.”

All of this was in the air during the New York City mayor’s Saturday evening press conference with Police Commissioner Bill Bratton, where he tried to ease tensions, despite a dramatic action from police at the event, who turned their backs when de Blasio spoke. The mayor called the killings a “particularly despicable act” that “tears at the very foundation of our society.” He called it an “attack on all of us.” “Our city is in mourning, our hearts are heavy,” he said. “We lost two good men who devoted their lives to protecting all of us.”

But for several politicians and police organizations, this call of solidarity wasn’t enough. “Our society stands safer because of the sacrifices officers make every day, but the hatred that has grown over the past few weeks in this country has gone unchecked by many elected leaders,” said the head of the New Jersey Policemen’s Benevolent Association in a statement on Facebook. “The blood of 2 executed police officers is on the hands of Mayor de Blasio,” tweeted the New York Sergeants Benevolent Association. Likewise, on Twitter, former New York Gov. George Pataki said he was “sickened by these barbaric acts, which sadly are a predictable outcome of divisive anti-cop rhetoric of #ericholder & #mayordeblasio.”

Lynch was even more inflammatory. “There is blood on many hands, from those that incited violence under the guise of protest to try to tear down what police officers do every day,” he said, addressing police outside the hospital where the slain officers were taken. “That blood on the hands starts on the steps of city hall in the office of the mayor.” In Baltimore, one lodge president in the Fraternal Order of Police gave a more expansive statement, blaming national officials for the violence. “Politicians and community leaders from President Obama, to Attorney General Holder, New York Mayor de Blasio, and Al Sharpton have, as the result of their lack of proper guidance, created the atmosphere of unnecessary hostility and peril that police officers now find added to the ordinary danger of their profession.”

And all of these sentiments were echoed by former NYC Mayor Rudy Giuliani. “We’ve had four months of propaganda starting with the president that everybody should hate the police,” said Giuliani during an appearance on Fox News on Sunday. “The protests are being embraced, the protests are being encouraged. The protests, even the ones that don’t lead to violence, a lot of them lead to violence, all of them lead to a conclusion. The police are bad, the police are racist. That is completely wrong.”

But these complaints aren’t true. Police officers aren’t under siege from hostile elected officials. At no point, for example, has de Blasio attacked the New York City Police Department. Instead, he’s called for improved policing, including better community relations and new training for “de-escalation” techniques. “Fundamental questions are being asked, and rightfully so,” he said at the beginning of the month, after the grand jury decision in the death of Eric Garner. “The way we go about policing has to change.”

Likewise, neither President Obama nor Attorney General Eric Holder has substantively criticized police. After a Ferguson, Missouri, grand jury declined to indict Officer Darren Wilson in the killing of Michael Brown, Obama appealed for calm and praised law enforcement for doing a “tough job.” “Understand,” he said, “our police officers put their lives on the line for us every single day. They’ve got a tough job to do to maintain public safety and hold accountable those who break the law.”

When directly asked if “African-American and Latino young people should fear the police,” Holder said no. “I don’t think that they should fear the police,” he said in an interview for New York magazine with MSNBC’s Joy-Ann Reid. “But I certainly think that we have to build up a better relationship between young people, people of color, and people in law enforcement.”

Even Al Sharpton supports cops. “We are not anti-police,” he said after the Wilson grand jury concluded. “If our children are wrong, arrest them. Don’t empty your gun and act like you had no other way.” And on this Sunday morning, Sharpton held an event where he and the Garner family condemned the cop killings in Brooklyn. “I’m standing here in sorrow over losing those two police officers,” said Garner’s mother. “Two police officers lost their lives senselessly.” The family of Michael Brown has condemned the shootings—“[We reject] any kind of violence directed toward members of law enforcement”—and in a statement, the chairwoman of the Congressional Black Caucus, Ohio Rep. Marcia Fudge, said, “This is not about race or affiliation, and it isn’t about black versus blue. All lives matter.”

Nothing here should be a surprise. Despite what these police organizations and their allies allege, there isn’t an anti-police movement in this country, or at least, none of any significance. The people demonstrating for Eric Garner and Michael Brown aren’t against police, they are for better policing. They want departments to treat their communities with respect, and they want accountability for officers who kill their neighbors without justification. When criminals kill law-abiding citizens, they’re punished. When criminals kill cops, they’re punished. But when cops kill citizens, the system breaks down and no one is held accountable. That is what people are protesting.

Given the dangers inherent to being a police officer—and the extent to which most cops are trying to do the best they can—it’s actually understandable that cops are a little angry with official and unofficial criticism. But they should know it comes with the territory. For all the leeway they receive, the police aren’t an inviolable force; they’re part of a public trust, accountable to elected leaders and the people who choose them. And in the same way that police have a responsibility to protect and secure the law, citizens have a responsibility to hold improper conduct to account.

Yes, this is contested terrain and both sides will fight to define the scope and limits of police power. But these arguments are a vital part of self-governance, which is why everyone should be disturbed by statements like Giuliani’s, Pataki’s, and Patrick Lynch’s. The idea that citizens can’t criticize police—that free speech excludes scrutiny of state violence—is disturbing. Since, if free speech doesn’t include the right to challenge the official use of force, then it isn’t really free speech.