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.

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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.’ ”

The shooting has handed But­tigieg the first significant challenge of his charmed campaign. To allies, his decision to leave the campaign trail and then hold two days of private meetings signals deliberate, considerate leadership. But to detractors, including many of South Bend’s black activists, his actions show that he still doesn’t get it.

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“How’s he handling it?” said Oliver Davis, the longest-serving black member of the South Bend Common Council. “Well, he talked to the media before the family. He skipped the family vigil, full of black residents. And then he then gave a speech to the police. So, how do you think that went over?”

On the campaign trail, But­tigieg has boasted of “transforming” South Bend into one of the nation’s “best-run” cities. But 40 percent of black residents here live below the poverty line. While downtown South Bend glows with new stores and restaurants, economic development has yet to arrive in most black neighborhoods on the outskirts of town.

The area where Logan died is somewhere in the middle, a historically black neighborhood near downtown where the old high school has been transformed into luxury apartments inhabited primarily by white residents. South Bend police say Logan was rummaging through cars in the parking lot outside those apartments about 3 a.m. Sunday when he was approached by Sgt. Ryan O’Neill. Logan flashed a knife, police said, and O’Neill opened fire.

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Late Sunday, Buttigieg appeared at news conference where he offered little new information about the shooting. “We’ve had prior cases of use-of-force incidents and officer-involved shootings where I hesitated, frankly, to get in front of cameras because we didn’t know very much and it was out of our hands,” he said. “But what I learned, what I was told by people in the community, is that it is important to open channels of communication.”

When asked whether he planned to open channels to the Logan family — who were waiting at that moment in the next room — Buttigieg was noncommittal. He wound up speaking briefly with the family, but the meeting ended after they grew frustrated with Buttigieg’s inability to provide information and his lack of compassion, friends of the family said.

“(He) ain’t done nothing,” Logan’s mother, Shirley Newbill, later recounted. “He ain’t recognize me as the mother of nothing. He didn’t say nothing to me.”

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The next morning, Buttigieg huddled with 25 leaders from South Bend’s black and Hispanic neighborhoods at a regularly scheduled community roundtable at the city’s Civil Rights Heritage Museum. After speaking briefly, Buttigieg opened the floor to questions.

“Mayor Pete . . . has been transparent thus far, and we are working together,” one attendee, the Rev. Michael Patton, president of the local NAACP chapter, said after the meeting.

But a number of younger community organizers and more outspoken black activists were excluded. Buttigieg’s failure to appear at the Monday night vigil further enraged critics who have been skeptical of Buttigieg since he fired the city’s first black police chief, Darryl Boykins, soon after taking office in 2012.

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“If you spill milk on the ground, and you wipe it up, it doesn’t stink. But if you let the milk stay on the ground, it goes sour and stinks up the room,” said Davis, the common council member. “Mayor Pete let the milk stay on the ground and stink up the room.”

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By Wednesday, Buttigieg was saying all the right things. At the swearing-in at police headquarters, he lamented that “years working to build trust between city leaders, public safety officers and members of the community we are charged to serve . . . are in jeopardy” because of the shooting. He noted the community’s frustration that police body cameras had not captured video of Logan’s death and urged officers to remember that they serve in a profession that has at times been the enforcer of racial inequity.

“You are choosing this line of work at a moment when our nation is facing the long shadow of a complex history around policing,” he told the newly sworn officers. “We are facing the consequences not just of distant historical wrongs, but of things happening in our present — a seemingly constant series of stories and videos from around the country showing abuses that tarnish the badge and fuel mistrust.”

Left unmentioned was the demographic makeup of South Bend’s newest police class: All six cadets were white.