Instead of showcasing But­tigieg’s ability to lead through a crisis, however, the shooting is exposing what has long been considered an Achilles’ heel of his candidacy: his frosty relationship with South Bend’s black residents. Since arriving on Sunday, Buttigieg has alienated the family of the dead man, Eric Logan, 54, skipped a vigil at the scene of the shooting, and sought advice from outsiders, including the Rev. Al Sharpton of New York.

On Wednesday, Buttigieg finally made his first extended public remarks about the shooting, appearing at South Bend police headquarters to lecture the city’s new cadet class about the importance of turning on their body cameras when they interact with members of the public. During Sunday’s shooting, the officer’s camera had been turned off.

“This is his nightmare,” said Jorden Gieger, a community organizer who is close to Logan’s family. “You have to imagine the first thing he said to the police chief was, ‘You all had one job: Don’t shoot a black guy while I’m running for president.’ ”