Each of us has probably at some point made that one serious mistake that has potentially grave implications. While we wrestle with the feelings of dread that overcome us in such moments, we pray for forgiveness and hope to be given a chance to make amends.

Some mistakes made by others are easy to identify as inadvertent. And then there are those that can be extremely difficult to categorize as innocent or intentional, because being able to make the distinction requires reaching inside the mind of the perpetrator. The recent incident involving Amy Cooper and Christian Cooper (no relation) is a prime example.

Mr. Cooper, a black man and an avid birder, was birdwatching in New York City’s Central Park when he encountered Ms. Cooper and her unleashed dog. After he began filming her on his cell phone following her refusal to put the dog on a leash as required by the park’s rules, she called the police, hysterically telling them that an African-American man was threatening her life. When the police arrived, they determined that the two had merely engaged in a verbal confrontation, and decided not to issue summons or make an arrest.

The huge public outcry that followed the release of the video of the encounter led to Ms. Cooper’s employer, Franklin Templeton, firing her from her position as head of insurance portfolio management at the firm. She issued a written apology to Mr. Cooper, in which she took responsibility for her actions. In a subsequent television interview, Mr. Cooper accepted the apology, saying that he didn’t think her life should be torn so completely apart in such a short time.

News of the brutal killing of George Floyd, a black man, by a white police officer in Minneapolis came out about the same time that the encounter between Mr. Cooper and Ms. Cooper occurred. The Minneapolis officer and three colleagues were responding to a call about a forgery taking place in the area where Mr. Floyd had been sitting in a vehicle. They handcuffed him and placed him face-down on the ground. Inexplicably, one of the officers then pressed his knee on Mr. Floyd’s neck, pinning his head onto the concrete floor for nine minutes, all the while ignoring Mr. Floyd’s desperate pleas that he couldn’t breathe. He was suffocated.

With the chilling video footage of that killing still fresh in my mind, I was initially inclined to disagree with what I considered to be a rather benign view taken by Mr. Cooper of Ms. Cooper’s actions. Fortunately for him, the police who responded to her call acted professionally when they arrived, as indeed the majority of police officers in America do. However, it is also quite possible that things could have ended up very badly for him had a different type of officer, perhaps in the mold of Mr. Floyd’s killer, been dispatched instead.

After carefully reading Ms. Cooper’s statement, though, and spending some time to reflect on it, I had a change of heart. I concluded that the magnanimity shown by Mr. Cooper was actually admirable. At the end of her statement, Ms. Cooper wrote: “I hope that a few mortifying seconds in a lifetime of forty years will not define me in his eyes and that he will accept my sincere apology.” I was particularly struck by that.

Ms. Cooper’s behavior, which undoubtedly was egregious, could very well have truly resulted from a spur-of-the-moment decision, as she said. While it is impossible for the rest of us to ascertain the veracity of that claim, objectivity requires us to try to look at her actions in that context and make our judgments accordingly. Moreover, even if those actions were triggered by some deeply ingrained racial prejudice, it is also true that we are all products of the environments in which we existed during our formative years. Refusing to accept her apology, therefore, would be tantamount to asking her to shoulder responsibility for the sins of an entire segment of society.

As cities across America burn, with protesters expressing their anger in good and bad ways and demanding justice for the families of Mr. Floyd and other unarmed black men killed recently, the need for peacemakers is greater now than ever. The best advocate for a cause is often someone whose consciousness on that issue has been awakened by a traumatic experience. Given what they have both been through over the last several days, Ms. Cooper and Mr. Cooper could play a very useful role in discussions about race in America.

I don’t know what is in store for Ms. Cooper in the coming weeks and months, but perhaps after the dust settles, she could use her newfound awareness to speak candidly about some of her inner feelings on race relations prior to the incident, and some of the things she has learned upon reflection in its aftermath. Mr. Cooper, on his part, has something valuable to teach all of us about forgiveness. They could make joint appearances to share their thoughts with audiences. I sincerely hope that they both seize this opportunity to fill a part of the leadership vacuum that, sadly, exists in America when it comes to the issue of healing racial divisions.