I think that Roth definitely took Green's killing personally but he would have been willing to "let it go" were it not for the fact that Michael was now moving in on Roth's business. That must have brought up all sorts of negative feelings.
"When the snows fall and the white winds blow, the lone wolf dies but the pack survives."
Winter is Coming
Now this is the Law of the Jungle—as old and as true as the sky; And the wolf that shall keep it may prosper, but the wolf that shall break it must die.
As the creeper that girdles the tree-trunk, the Law runneth forward and back; For the strength of the Pack is the Wolf, and the strength of the Wolf is the Pack.
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