AP Photo

It has never been a secret that Osaka Mayor Toru Hashimoto’s father was ayakuza, or that his gangster father hailed from a social underclass that has often been discriminated against in past years. Newspaper and magazine articles have alluded to this without making much of an issue of it -- until now.

The mayor, who aspires to turn his regional-based political party into a national force, went ballistic recently over a magazine article that he said delved unfairly into his family’s past using...