Cosell's most famous interviews were with Muhammad Ali. The verbally precocious pair developed a friendship that was strengthened by controversy. Cosell was the first sportscaster to call the heavyweight champion, originally known as Cassius Clay, by his new Muslim name. This act alone was scandalous to many Americans. In 1967 when Ali refused for religious reasons to be drafted to fight in Vietnam, Cosell was irate about the New York State Boxing Commission taking away his championship. "What the government did to this man was inhuman and illegal under the Fifth and Fourteenth Amendments," he was quoted in a Washington Post obituary; "Nobody says a damned word about the professional football players who dodged the draft. But Muhammad was different; he was black and he was boastful." Some would discount the relationship between the two men by saying that Cosell knowingly rode to fame on Ali's coattails. Looking back decades later, essayist Stanley Crouch listed it among Ali's major accomplishments, asserting in Time Atlantic that "in his relationship with the Jewish sportscaster Howard Cosell, Ali realized the ongoing dream of our society—and perhaps the world—that people of different colors and religious backgrounds can disagree, taunt each other, support each other and at almost every point so purely recognize the humanity of each other that a transcendent friendship can emerge."
It was important for Cosell to show the same issues that trouble the world at large were also to be found inside sports. "I have sought to bring to the American people a sense of the athlete as a human being and not as a piece of cereal-box mythology," he told Playboy. He wanted dispel the idea that "sport is somehow different, that it's a privileged sanctuary from real life, a looking-glass world unto itself." Racism and drug use were two of the "real world" issues Cosell explored. The ABC radio sports director Shelby Whitfield commented in a People magazine retrospective, "When Howard came on the scene … no one criticized referees or coaches or players or anybody. But he was a lawyer, and that went to the core of everything." Other legal issues that Cosell weighed in on were Curt Flood's challenge of baseball's reserve clause and the 1986 USFL lawsuit against the NFL.