Because Barzini was using Tattaligia to try to run the Corleone’s out of New York. This became obvious during the meeting of the 5 heads when Barzini took over for Tattaligia in telling Don Vito what the terms of the agreement would be. In acquiescing to Barzini in the meeting, Tattaligia showed that he was just the foil being used to attempt to force the Corleone’s out.
It was very subtle and was something that I did not pick up on the first few times that I watched the movie.
Thanks Delta. That explanation makes sense. Another thing that always puzzled me was in Godfather II - why was Frankie Pentangeli still getting special treatment from the FBI after he didn’t rat out Mikey at the Senate hearing. Seems to me that after that happened, they’d let him rot in jail forever.