Even though Roth admits the killing of Green was "bsiness," it is very clear his bad feelings for Michae were not about business, but strictly personal.
And that is what made him a great gangster. Just like Vito Corleone (and later, Michael) they all took everything personal.
In the novel they aadmit this, but on screen they never do.
"Io sono stanco, sono imbigliato, and I wan't everyone here to know, there ain't gonna be no trouble from me..Don Corleone..Cicc' a port!"
