sorry you are wrong too.
Nurgle is about keeping things the same, about stagnation, yes he is about "everyone dies" and being locked into that fate irks tzeetch, but the main reason tzeetch and nurgle hate each other is because one is stagnation and the other is constant change.
tzeetch hates Khorne because Tzeetch is all about planning, big strategies, chess, Khorne hates that, he takes an axe to chess boards, his champion actually kills anyone around him that actually tries to use strategy instead of just rush that hill and kill everyone.
nurgle hates slaanesh because of the whole isha thing, and because the love and good feelings slaanesh gives isn't real, it is all chemical, where as Nurgle LOVES his children, he is their daddy.
Khorne hates nurgle because Khorne is about the strong, if you are strong, fight that man and kill him, only the strong survive. diseases, similar to sorcery, don't care, they cut down the greatest warriors right along side the weaklings, and Khorne hates that.
Slaanesh hates Khorne because Slaanesh is about the sensations and the WHY and HOW you are doing something, while Khorne is all about the doing. Khorne is single minded in the extreme while slaanesh focuses on open minded and experimentation.