Some great points and thoughts being brought up in this thread.
I was trying to think about things from Kyrie's perspective (since I generally only think about them from my own/a fan's perspective). I could see where Kyrie feels he is actually in somewhat of a tough spot. This season just showed him that the team as currently constituted can't win a title, maybe not for talent reasons but certainly based on cohesiveness, acceptance of roles, etc. So there is no point in just running it back - which I don't think Kyrie or the team would do anyway.
On the other hand, if the C's do pull off a trade for AD, he's likely to only be here for one year, in which case Kyrie would be stuck on a team with even fewer assets and talent than he had this past year. Some have proposed he take a 1+1, which I suppose is possible, but does he want to take that financial/injury risk, and also does he want to have to go through this whole process again in a year?
If AD wanted to play here and it was clear he would make a long term commitment, IMO, I think Kyrie would be fully on board. But given what DA will have to give up to get AD, and then the prospect that he will be gone in one season, I think puts Kyrie in an extremely difficult position to stay.
Then again, maybe this is all wrong, and he just wants to go back home, play in a different system, or some other reason we haven't yet heard about.