I can think of two other not dissimilar instances

• Vito sending Luca to find out what the Tattaglia's had under their finger nails thus to Luca's death

Vito was slipping

• Greene slapping Fredo around in public

Corleones were acting weak

Michael taking the Rosatos side against his own man Pentangeli is inexcusable, on so many fronts and nice reward! indeed for loyal Pentangeli

• Pentangeli was loyal to Vito, Michael's father [and Michel himself] for years
• Rosatos were taking hostages [not sure what this means?]
• Rosatos spit right in Pentangeli's [Michael's man] face
• Roth from Miami was openly backing the Rosatos, the Corleone rivals in New York against the Corleone people, in effect against Michael
• Roth was not even subtle about his backing of the Rosatos

Clemenza supposedly promising the Rosato brothers, Corleone rivals, three territories in the Bronx after he died and Pentangeli not honouring Clemenza's 'promise'
Michael wants Pentangeli to be fair with the Rosatos because they feel cheated

Then the true reason surfaces that Michael doesn't want the Rosatos touched because the Rosatos are backed by Roth with whom Michael has business that's important and doesn't want it disturbed

Michael threw Pentangeli under the bus and then played Pentangeli like a violin, hounding him to his suicide via Tom

Whilst Pentangeli should have had more faith in his Don, with Dons like Michael who needs....