As a commanding officer for a sheriff’s office staffed by 300 sworn deputies just outside the Washington, D.C., beltway, there was too much opportunity for Jeff Wood to experience the worst in people.

It’s part of a vicious cycle for law enforcement officers in high-crime, urban areas, who can present a steely front because of the types of delinquency and people they encounter day in and day out, who in turn can be distrustful of those in positions of authority because they’re standoff-is...