Aww. I think your feelings got a little more hurt than I'd intended to. Not that I intended to hurt them at all -- but its clear you didn't actually scratch even a little beneath the surface on some of the things Thanaton actually said. So let me make it a little more clear for you.
This is the most important part of it all: Thanaton is a hypocrite. A huge one. That his actions are in direct contradition of his stated beliefs is not exactly super surprising. He demonsrtrates his capacity for intense hypocracy several times through the stories, nor do many other Sith seem to share this view of the world with him.
Thanaton is, yes, a hypocrite. He's a slavishly devoted to Sith traditions, especially when they're convenient to him, and is perfectly willing to find excuses to shun them when they're not. He honestly wants you to die because you're part of the legacy of Zash. Zash, incidentally, whose obvious murder of his own minion in Skotia (who worked for Thanaton, recall) *made him look bad*. It's not just the law. It's pretty clear, when he talks about several times how 'A Sith that can't protect his own powerbase isn't any kind of Sith at all".
When Zash murdered Skotia, through you, explicitly countermanding Thanaton's direct orders to her, it *made him look bad*. That's the real reason he was plotting to get rid of Zash (something Zash and you take care of for him) and the reason he's getting rid of you. It's not just the 'law' (recall, incidentally, that the power bases of other Sith are destroyed during Sith internecine warfare on a regular base and that this fact is actually mentioned in several codexes) but also a matter of personal pride. You made Thanaton look bad. You made people doubt his capacity to maintain order amongst his underlings and to protect his own powerbase. That Zash did it in a highly sloppy and disrespectful way to him personally is just salt on the wounds that you're a constant, nagging reminder of. All the conservatism and crying about the law and more is really just garbage hiding his real motivation: a desperate fear of being seen as weak. It really -isn't- personal for him, at least at the start, but as long as you're alive, you're a living reminder of his own weakness and his own fear of being *seen* as weak by the others.
Its this fear that drives him, as fear drives all Sith. I mean, it's the chief passion they rely on as part of the Dark Side.
That he ultimately makes the same kind of move on his own superior that Zash did on Skotia only shows the depths to which his hypocracy sinks. It's okay when *he* does it. But it's not okay when its disrespectful to *him*.
Anyways, like I said: There are plenty of problems in this story. Thanaton's motivations aren't one of them, nor are his justifcations for killing you. They're not explicitly stated as clearly as they perhaps could be, but it *is* there, beneath the surface.
I've got my own beefs with the SI story, though.