NEW YORK—Eric Garner was overweight and in poor health. He was a nuisance to shop owners who complained about him selling untaxed cigarettes on the street. When police came to arrest him, he resisted. And if he could repeatedly say, “I can’t breathe,” it means he could breathe.

Rank-and-file New York City police officers and their supporters have been making such arguments even before a grand jury decided against charges in Garner’s death, saying the possibility that he contributed to his own demise has been drowned out in the furor over race and law enforcement.

Officers say the outcry has left them feeling betrayed and demonized by everyone from the president and the mayor to throngs of protesters who scream at them on the street.

“Police officers feel like they are being thrown under the bus,” said Patrick Lynch, president of the police union.

The grand jury this week cleared a white patrolman, Daniel Pantaleo, who was caught on video applying what appeared to be an illegal chokehold on the black man. Mayor Bill de Blasio said the case underscores the NYPD’s need to improve relations with minorities.

But Lynch said: “What we did not hear is this: You cannot go out and break the law. What we did not hear is that you cannot resist arrest. That’s a crime.”

At the noisy demonstrations that have broken out over the past few days, protesters have confronted police who had nothing to do with the case. Signs read: “NYPD: Blood on your hands,” “Racism kills” and “Hey officers, choke me or shoot me.” Some demonstrators shouted, “NYPD pigs!” More than 280 people have been arrested, and more demonstrations were planned Friday.

In private and on Internet chat rooms, officers say they feel demoralized, misunderstood and “all alone.”

Some are advising each other that the best way to preserve their careers is to stop making arrests like that of Garner’s, in defiance of the NYPD’s campaign of cracking down on minor “quality of life” offences as a way to discourage serious crime.

“Everyone is just demonizing the police,” said Maki Haberfeld, a professor of police studies at John Jay College of criminal justice. “But police follow orders and laws. Nobody talks about the responsibility of the politicians to explain to the community why quality-of-life enforcement is necessary.”

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The fatal encounter occurred in July after Pantaleo and other police officers responded to complaints about Garner, a heavyset 43-year-old father of six.

The video showed Garner telling officers to leave him alone and refusing to be handcuffed. Pantaleo, an eight-year veteran, appeared to wrap his arm around Garner’s neck and take him down to the ground with the help of other officers.

Garner could be heard saying, “I can’t breathe,” several times before he went motionless.

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The medical examiner later found that a chokehold resulted in Garner’s death, but also that asthma, obesity and cardiovascular disease were contributing factors.

While many have decried the death of another black man at the hands of a white officer, no evidence has come to light to suggest that Pantaleo’s actions were racially motivated. His supervising sergeant at the scene was black, and so were some of the officers involved in the confrontation.

As the video sparked accusations of excessive force, the police unions mounted a counter-narrative: that Garner would still be alive if he had obeyed orders, that his poor health was the main cause of his death and that Pantaleo had used an authorized takedown move — more like a headlock than a chokehold — to subdue him.

While the grand jury proceedings were secret, Pantaleo’s lawyer has said that the officer testified that he never tried to choke Garner and did not believe the man was in mortal danger.