They tried to blackmail MLK to get him to kill himself. A department created originally to fight the mob started acting exactly like it. There's no way a reasonable person's faith in an organization like that could ever be restored.
Imagine the information that isn't public about their misdeeds.
The FBI repeatedly denied that the Mob existed for over a decade, until a patrol cop stumbled accidentally on a meeting of Mob bosses from across America.
J Edger Hoover's Wikipedia:
> From the mid-1940s through the mid-50s, he paid little attention to criminal vice rackets such as illegal drugs, prostitution, extortion, and flatly denied the existence of the Mafia in the United States. In the 1950s, evidence of the FBI's unwillingness to investigate the Mafia became a topic of public criticism.
Imagine the information that isn't public about their misdeeds.