He didn't respect Lefty, but I think he saw a clear and strong rival in Sonny Black.
I love the scene in the disco/club when one of Sonny Red's group makes a joke about Sonny Black and they all laugh.
The look they share afterwards speaks volumes. Sonny Red knew he'd beep up badly and made an enemy.

Same family yes but at the time the movie is set the Bonnano family were in turmoil and had even been disowned by the commission. In the confusion a power struggle ensued and Sonny Red was actually attempting to seize power from the boss. It was Sonny Black with the permission of the other families who was tasked with executing him and his two associates.
Hey! You're not old enough to drink! Now go and die for your country!!!

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Mob politics I guess. People's allegiances are as thin as a tissue in their world. It has to be if they hope to survive. You end up backing the wrong horse for too long and you find yourself starring down the business ned of a gun for no other reason than you might be a problem later on. Horrible world and I'm glad they showed this aspect of it.

As far as I remember reading, Sonny Red wanted to take over when the boss Carmine Galante was murdered. But he had to go under Rusty (in the can) Rustelli, who Sonny Black was loyal to.
He then tried to take over with the 2 other captains again and they were killed as seen in the movie.
Well she turned me in to a newt! I got better!