where did it come from? it came from thousands of years of sith having to live together with out whiping them selves completely out. backstabs betrayals are all great and incouraged as long as they follow the tradition/ rules that gareenteed that you actually had to work for it. it also came from a sith's natural caution and fear of retribution. That in a sense is what thanaton fears is that if the tradition isn't followed sith will just throw caution to the wind and murder each other until nothing remains.
thanaton liked those betrayals and backstabs becuase they followed the tradition thanaton is talking about like i said there are clear rules to how such things should be done.
karrid had to make gravius fire the first shot she couldn't just blast him or rather she could but it'd break the tradition. Nox won a traditional battle who's whole reason for exisisting was for just such an occasion. thanaton's tradition is basically the reason why sith can stay in power with out killing some one every two seconds it's why sith that meet each other don't instantly fight.
by the way are you sure he liked naga shadow? i know he liked tulak hord and i think he liked ludo kressh (or maybe he was just noting that he participated in the ritual fight i can;t remeber) but i don;t think he likes naga shadow.
Sith's society is all about cruelty and power, betrayal is a way to achieve the real power, Zash had conflict with Darth Skotia before the SI story started, his apprentice even wanted to kill Nox.
But it's clear that everyone in the council knew Karrid was trying to let Gravus(He was totally different than the calm commander we saw on Taris) shoot her, but they still accepted her because she proved her power.
The codex showed he liked Sadow.