För att undvika retribution för hans förräderi av familjen Corleone som faller på Frankies barn & familj.
Obs! Det var Tom som berättade historien, inte Frank.
Från Wikipedia
After the [Senate] hearing, consigliere Tom Hagen (Robert Duvall) visits Frank in custody. Hagen tells Frank that he did the right thing by recanting. Tom and Pentangeli talk nostalgically about the good old days when the Corleone Family, as Pentangeli says, "was like the Roman Empire." Hagen tells a story about what would happen to traitors during those Roman days, implying that the correct thing for Pentangeli to do now is to kill himself. Hagen tells Pentangeli if he accepts responsibility for turning on the Corleone family and kills himself, Frank's family will always be taken care of, just as the families of confessed traitors in the Roman days who killed themselves were allowed to keep all of their possessions. He thanks Hagen, returns to his assigned quarters, and despite the presence in the other room of his federal guards, commits suicide by slitting his wrists while taking a bath.
The finished film leaves unclear exactly what about his brother [Vincenzo]'s presence [at the hearings] motivated Frank to change his story. The final film only states that Vincenzo is a powerful and ruthless Mafia chieftain in Sicily.
An early draft of the film's script explains that Vincenzo, shocked that Frankie is about to break his blood oath and betray the Corleones to government authorities, attends the hearing to remind Frankie that he must not break the Mafia's code of silence, omertà. His brother's presence [at the Senate hearing], as well as the stare they exchanged, serves as a threat that if Frankie follows through with his planned testimony, retribution will be taken against his children, who are living in Sicily under Vincenzo's guardianship.