Some experts argue that a single genocidal action does not necessarily equate to genocide. The question then becomes how many genocidal acts does it take to make recognizable genocide?
Cain's action, as you capably argue, was murder, not genocide.
Your point is well taken. Reasonable people can argue that the actions of Sherman and Chivington - in killing Indian men, women, and children - were like Cain's action: just murder not genocide.
Mass murder, for sure, and criminal by any definition, but still not full-on genocide.
I don't necessarily agree with that argument because I know of Sherman's earlier advocacy of exterminating men, women, and children during Lincoln's War.
But to argue Sherman's and Chivington’s actions in killing Indian men, women and children were mass murderer and not genocide - yes, there is a reasonable argument for that position based on order of magnitude.
Your words quoting Sherman's letter to Grant notwithstanding, I've seen no evidence, none, of Sherman committing "mass murder", "extermination", "genocide" or "war crimes".
I'm not saying here that every one of the 52-some wars between the US and Native American tribes was conducted strictly according to Marquees of Queensbury rules, certainly not.
But politically motivated lurid accusations are not the same thing as real history.
And you well know it.