Kenya Barris, the creator of the ABC family sitcom “black-ish,” slumped on a sofa in his airy home, in Encino, California, his eyelids drooping with fatigue. In the nearby media room, his two young sons, Beau and Kass, played Minecraft on an Xbox. In the kitchen, his wife, Rainbow, who was pregnant with their sixth child, made popcorn. Out in the hall, their three daughters—aged ten, fourteen, and sixteen—yakked and giggled. The family was getting ready to watch the West Coast airing of “Hope,” an episode about police racism which, at varying times, Barris had described to me as both “the one that ruins me” and “maybe my most important episode.” Once, with a resigned shrug, he had said, “Well, the toothpaste is out of the tube.”

Like most breakthrough sitcoms, “black-ish” is built on autobiography. It’s narrated by Andre (Dre) Johnson, a black ad executive, played by Anthony Anderson, who has jumped, as Barris did, from inner-city poverty to bourgeois wealth, only to find himself flummoxed by his brood of privileged, Obama-era kids. Tracee Ellis Ross plays his wife, who, like the real Rainbow, is a biracial anesthesiologist nicknamed Bow. With a joke velocity approaching that of “30 Rock,” the show, brassy and shrewd, stands out for its rare directness about race and class. As Barris likes to put it, whereas “The Cosby Show” was about a family that happened to be black, “black-ish” is about a black family.

In its first two seasons, the show scored laughs from such subjects as whether black parents spank more and how different generations use the N-word; there was a plot about the knowing nod of recognition black men give one another. One hilariously nervy script satirized Martin Luther King Day. (Dre, Jr., admits that he’s never read King’s speech, explaining, “I always kind of zone out when people start to tell me about their dreams.”) Some viewers, especially black ones, have been put off by the show’s title, with its cheeky implication that some people are less black than others. But Barris told me that he was glad he’d resisted ABC’s suggestions to sanitize it, titling it “The Johnsons”—or, absurdly, “Urban Family.” Michelle Obama has called “black-ish” her favorite television show.

Until “Hope,” however, the show hadn’t tangled with real-world politics. During Season One, in 2014, Barris pitched a story based on the arrest of the African-American professor Henry Louis Gates, Jr., for breaking into his own home. At the time, the Ferguson riots were streaming live on the Internet; ABC asked him not to do any jokes about cops. By 2015, the national outcry about police brutality had become too loud to ignore—and “black-ish” was getting raves as part of a newly diverse TV landscape. Over the December holidays, Barris holed up in the studio attached to his home, bingeing on Red Bull and “probably some Adderall,” and hammered out “Hope.”

The episode opened with Marvin Gaye’s “Inner City Blues (Make Me Wanna Holler)” and a scene borrowed from Barris’s life: Beau, watching the Ferguson riots on television, had asked his parents, “Why are these people so mad?” What followed was a classic TV “bottle episode,” set in one location: in their living room, the family debated the acquittal of a cop who’d repeatedly Tasered an unarmed black man. Their arguments were punctuated by jokes about Dre’s father having been a member of something called the Black Bobcats. (“We were Panther-adjacent.”) The episode felt haunted—and was made more vital and angrier—by the killing of twelve-year-old Tamir Rice, in Cleveland. While Barris was struggling with the script, the Ohio prosecutor announced that a grand jury would not indict the cops who shot Rice. Barris still gets distressed talking about the case. “You know, twelve is young,” he said, his voice cracking. “That’s somebody’s baby still.”

Eight-year-old Beau, who was wearing pajamas printed with pine trees, hopped onto his father’s lap. While another ABC sitcom, “Modern Family,” played on the TV, interspersed with promos for “Hope,” Beau held his father’s iPhone, watching a nature video about predators.

“It escaped!” Beau called out, looking up at his dad excitedly. “Mouse can swim?”

“What?” Barris said, confused. Forty-one years old, he has amused, hooded eyes and pockmarked cheeks. Blue-green tattoos peek out from his collar.

“Mouse can swim?”

“No, mice can’t swim—they can, like, paddle,” Barris said, laughing.

In the video, a mouse was in a river, being tormented by a fish. “That’s mean, now,” Barris said. “That’s sadistic.”

“Why are they mean?” Beau asked.

“Guys do that sometimes. It’s a bad way to be.”

“It’s gonna escape. Look!” Beau said.

“It didn’t escape,” Barris said, gently. But Beau kept seeing something different.

“Yes,” he insisted. “It did.”

“. . . and will to the best of my ability, which is terrific ability, by the way. Everyone agrees, I have fantastic ability. So there’s no problem with my ability, believe me. . . .” Facebook

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The exchange felt peculiarly congruent with the episode we were about to watch: a meditation on just how much black parents should protect their children’s innocence about the American justice system. Barris, who had been thrown against cars by cops and seen friends choked during arrests, had devoured Ta-Nehisi Coates’s book “Between the World and Me,” an anguished manifesto addressed to Coates’s son; the book was both quoted and displayed in the episode. (Barris asked Coates to do a cameo, but Coates declined.) The show’s climax came when Dre begged Bow to remember how thrilling it had felt to watch the Obamas walk into the White House for the first time—and how terrified they were that the First Couple would be assassinated. “Tell me you weren’t worried that someone was gonna snatch that hope away from us, like they always do,” Dre said. Silent footage was spliced into the scene: the Obamas, smiling, youthful, a model American family.

The table read for “Hope” had been cathartic; afterward, Laurence Fishburne and Jenifer Lewis, who played the Johnson grandparents, made speeches thanking Barris for writing it. But Barris knew that the episode was odd—not especially funny and possibly pedantic. “I played it for friends, and no one’s going to say they don’t like it to your face,” Barris told me. “But the reactions have been mixed.” He worried that it might be perceived as agitprop, a Black Lives Matter episode; although he supported the movement, he wasn’t a fan of the idiom. “It’s alienating,” he told me. “No civil-rights movement has gotten anywhere without the help of white liberals.”

These worries were intensified by some Westeros-style drama at Disney, which owns ABC. A week earlier, Barris’s strongest ally—the network’s president, Paul Lee, the British executive who had bought “black-ish”—had been ousted. Ben Sherwood, the president of Disney-ABC Television Group, replaced Lee, who is white, with Lee’s deputy, Channing Dungey. She became the first black network president in history, a benchmark that got gushing press. But Barris didn’t know Dungey; he had no idea what to expect. It wasn’t a great moment for an episode to misfire with the show’s audience, which is three-quarters nonblack. On Monday, Barris said, he had called ABC to make sure that its promos prepped viewers for, “as much as I don’t want to say this, a ‘very special episode.’ ” He added, “They did a good job.”

Now that the East Coast airing was over, it was clear that “Hope” was a phenomenon: it was trending on Twitter and being gif’d and quoted and hallelujah’d for its embrace of the Norman Lear tradition of political theatre. “So many people I went to school with, that I hadn’t talked to since elementary school,” Barris marvelled, reading his e-mail. He looked for negative responses, too: “On Facebook, I got scared, because I saw people saying, ‘I’ll never watch the show again.’ That’s the last thing I need right now.”