With Kayn and Rhaast, you do realise the way the 2 talk to each other is basically a fake-out contest, right?
They're both plotting and trying to kill each other in the same manner as 2 split personalities inside a body are somehow trying to off each other, and unlike most cases of split personality disorder where the split persona often have no real connection with each other besides sharing the same body, Kayn and Rhaast are mentally connected and capable of actually sensing each other's intent and emotion. Do you know how hard it is for you to get rid of someone under this kind of circumstance?
Ofc they try to deceive each other by playing the buddy game, that's the most fucked up part of their seemingly "tough love" relationship, that it's basically entirely fake and front to cover each other's end game of trying to get rid off another; imagine 2 friends who are only friends in the first place because they want to kill the other guy, and actually do it when they get the chance to so no movie plots like 'oh they actually become friends', none of that, only fake relationship aiming for the kill. Kayn is trying to find a way to erase Rhaast's persona and take the power entirely his, Rhaast is trying to survive until the corruption finishes its job and remake Kayn's body into a vessel of his own choosing with the Kayn's ego similarly erased.
The fake-out is so nasty they even openly tease each other that they are going to kill them as just some kind of joke they throw at each other (Rhaast would trashtalk Kayn and simply demand him to give up his body and soul, Kayn would taunt Rhaast and claim that he's going to kill him before he is killed), which is again, what they actually do once they have the right cards as shown in the gameplay. Let it sink in.