George Zimmerman is a disturbed and dangerous man. He is a man with a prolonged history of violence and poor judgment, who is yet to demonstrate remorse for taking the life of an innocent 17-year-old boy. The police chief who oversees Zimmerman's former Florida town agreed with a concerned citizen who wrote that Zimmerman was "a Sandy Hook [or] Aurora waiting to happen".

This past summer Zimmerman was pulled over for speeding twice, and he participated in what appears to be a staged car crash rescue to repair his soiled public image. His recent arrest and felony charge for assaulting his girlfriend and threatening her with a firearm was met with little surprise by those of us who were devastated by outcome of the Trayvon Martin murder trial.

As evidence mounts that Zimmerman is a menace to society, his character will come under increasing attack. These too-little-too-late public condemnations may feel like vindication in light of the injustice of the Trayvon Martin tragedy. But left unchecked, shouts of "I told you so!" will drown out the most crucial lessons of the saga. Zimmerman's personal failings and poor character played undeniable roles in Martin's death. But the injustice of the Martin murder is not enabled or sustained by "bad guys" like Zimmerman. Rather, it is produced by a broken criminal punishment system that reflects a society rife with institutional racism and prejudice against people of color.

During the murder trial, defense attorney Mark O'Mara explicitly told the jury, "Do not give anybody the benefit of the doubt except for George Zimmerman." Indeed, Zimmerman was given the benefit of the doubt by the legal system at every turn, and it began long before the trial started. It took sustained protests by Martin's parents, neighbors, and prominent civil rights advocates merely for Martin's killer to be arrested and brought to court.

The presumption of white innocence is interwoven with the perceptions of black and Hispanic criminality and threat. Law professors Allie Rolnick and Priscilla Ocen explain that self-defense laws like "Stand Your Ground" are based on the idea of "reasonable fear" of severe bodily damage. So Zimmerman's "not guilty" verdict cannot be separated from condemnation of Martin as fearsome, despite the fact that Zimmerman pursued Martin in a vehicle and confronted the boy with a loaded gun. These codependent biases of white innocence and black guilt were crystalized through comparisons between Zimmerman (who is Hispanic but was perceived as white) and Marissa Alexander, a young black woman who was sent to prison after her "Stand Your Ground" defense claim was denied. Alexander, who fired warning shots to scare off her allegedly abusive husband, had her case reopened after the Zimmerman verdict.

The plague of racial prejudice is not speculation. Stereotypes of black criminality run rampant and are empirically documented (pdf). Implicit and explicit racial prejudice against blacks and Hispanics has increased since President Obama took office in 2008. But the most disastrous impact of prejudice is not social unpleasantness, it is its codification and reinforcement in institutions like the police system and the courts.

New York City's "Stop and Frisk" policy and Arizona's immigrant surveillance law are two ongoing legal battles that exemplify these trends. Despite Obama's heartfelt response to the Zimmerman verdict, little action has been taken by the federal government and racial profiling and mass incarceration of blacks and Hispanics continues unchecked.

The idea that we can address Zimmerman's transgressions without talking about the interplay of race, gender, and class is often framed as a commitment to neutrality. Judge Debra Nelson, who presided over the Zimmerman trial, actually banned the phrase "racial profiling" from being used during proceedings. But silence about race, gender, and class is not neutrality. Colorblindness and "postracialism" require the active denial of continued oppression of people of color and the racist stigma that follows young black men and boys like Martin.

Zimmerman's latest arrest presents another opportunity for "neutrality" to manifest as active denial. Zimmerman's history of domestic violence cannot be treated as unrelated to his current predicament. As Salamishah Tillet pointed out during the murder trial, previous abuses of women and children are often precursors to repeat offenses, especially when left unchecked by the criminal punishment system.

We have to guard against attributing the Martin tragedy solely to Zimmerman's behavior and taking satisfaction in his disgrace. The Martin murder and the plague of domestic violence against women and children should inspire anger and righteous discontent. But rather than exhausting ourselves with calls to lock Zimmerman up and throw away the key, our indignation needs to be channeled and used as fuel for a long and unglamorous fight.

We have to reform immigration policy, ban racial profiling, and repeal sentencing laws that disproportionately penalize people of color. We also have change the ways we talk about criminal punishment, innocence, and white male privilege. Neutrality is a smokescreen for racism and sexism inscribed in law and on our bodies. So we have to talk truthfully about race, gender, and class in courts, legislative halls, schools, and in our homes if we are to move towards justice. Catching the bad guy will not stop the crime.

• This commentary was amended on 20 November to correct that Trayvon Martin was 17 years old.