Tywin’s argument is essentially that the RW would kill the northern cause for good and all and the war would be over, minimizing the casualty count in the long term. Unless I’m mistaken, and I could be, it’s the same skeleton of the argument that gets used when arguing for Hiroshima and Nagasaki. The difference is that when you join an army you knowingly sign up for the risk that you might die. When you’re a civilian you don’t. Those involved in the RW, besides Catelyn, are still an army, but they were in an arguably civilian setting. The RW was deception, whereas open war, well, isn’t. Does that fundamentally change the honorableness of killing? I don’t know, and I think Tywin brings up a compelling dilemma, a moral conundrum worth philosophizing over. If you do see the wedding feast as fundamentally indistinguishable from the battlefield, and if you don’t agree that all war is murder, then the only murder really committed is Catelyn, as far as I’m aware. But not everyone WILL agree that a wedding feast is fundamentally indistinguishable from a battlefield, and not everyone WILL agree that all killing in war is murder (otherwise Karstark’s sons were murdered by Jaime Lannister, no?).
But here’s the thing. If you agree that all war is murder, then what should Tywin have done for the greater good? CALL OFF THE FUCKING WAR. The only reason he won’t is he refuses to give up the utter supremacy of House Lannister over everyone else.
The debate I saw on asoiafuniversity said not that Tywin said that the RW was noble, but rather that war isn’t. I could agree with that (again though, I’m not sure what I think about all killing in war being murder, even though I’m very strongly anti-war … because I’m anti-violence and anti-killing). But I don’t agree that what Tywin did was really in the interest of the greater good, not in spirit, even if it did bring an end to a major arena of the war and even if you do buy the utilitarian argument that in the long run fewer people died. Because of the third option: peace.
PEACE IS ALWAYS AN OPTION!!!!
Tywin invoked this war in the first place, don’t forget that. Tywin flouted the king’s authority (everyone else has to go through the king, why the fuck not Tywin?) and set Gregor loose upon riverlands CIVILIANS, egging Edmure on into war. Tywin isn’t responsible for Stannis and Renly deciding to go to war, and it’s not his fault that Joffrey ordered Ned killed and earned the enduring enmity of the north, but Robb was going to come help the Tullys anyway, at the very least, so the open hostilities that happened in the duration of AGOT are pretty much, as far as I’m concerned, started by him. Furthermore, though he didn’t want Ned Stark dead, he doesn’t actually have to stop them from seceding in retaliation to Ned’s death. The reason he does? Power. Ultimately all the desires for dynastic power, while they seem proper and procedural when you start ASOIAF, slowly become obvious for the nakedly destructive and wantonly callous greeds that they are. If Tywin really cared about the greater good, he would have done what Edmure Tully did and put the lives of innocent civilians above dynastic strength in the first place. (This goes for other parties involved in the war too, not just Tywin Lannister.)
TL;DR Tywin Lannister made a fairly compelling ethical argument without really caring about the ethics of the scenario at all. In doing so he deflected Tyrion’s accusations, which was his only objective, because Tywin Lannister is the human form of Teflon.