I'm very confused by Irving's request. I get the idea that he wants to be THE MAN, but that is a stupid idea. No one is really a solo act in the NBA and accomplishes anything significant other than filling up the stat sheet. Ask Paul George how being the man went in Indiana. To be truly successful you have to be on a team with at least one other all-star, preferably two or three. Also, if all he was concerned about was being the top guy, why not just wait until LeBron presumably leaves after next season?
I think the most logical idea is that Kyrie knows that James is a goner and wants to get out ahead of the storm because he doesn't want to be stuck on a losing team. What compromises that idea is the list of teams he doled out; Minnesota, Miami, New York and San Antonio. The first three teams didn't even make the playoffs, and presumably they would have to give up substantial assets to land Irving. If Irving was afraid of being stuck on a losing team, I think the last team I would want to be headed to would be the Knicks.
The word right now is that Irving wants to be the top star and doesn't like playing with LeBron. There are plenty of great players who may not be very fun to play with, but James isn't one of them. Irving gets all the shots he wants and LeBron is happy to differ to him on offense, even when he is on the floor with him. Remember, Irving was the one who took the dagger three that really sealed the championship for Cleveland in Game 7 last year. That is the ultimate trust in a player; Kobe, MJ, Bird, Oscar or many other all-time players would have hated to differed to another player in that situation.
I think what really has motivated Irving here is more of an off-the-court storyline between James and the Cavs. Irving was drafted by Cleveland when they were terrible and put together some promising first few years. LeBron suddenly comes back and commandeers the team and becomes the sole focus of everything. Cleveland is LeBron and LeBron is Cleveland. Every move is made to satisfy LeBron, from giving Tristan Thompson a huge contract and overpaying JR Smith to mortgaging the future to bring in veterans like Korver, Channing Frye and Timofey Mozgov. I personally think Cleveland should try and go all-in on the LeBron years; but if you are Kyrie and the team has basically said they don't care about your prime and now you hear that James is leaving in a year and you have three more years on your deal and the team will have nothing to build around---that would piss anyone off a bit. Through in all the other weird LeBron stuff like getting Blatt fired, the odd subtweets, the shopping of various players, and just the overall cult of personality that swirls around him in Cleveland, and I can understand why Kyrie wants out.
At the end of the day though, Cleveland is just one KD foot injury or Curry sprained ankle from winning another championship. When you are this close I think you just have to suck it up and hold on for another year. If LeBron bolts after this year Kyrie is still a superstar in his prime with two more years on his deal, Cleveland can always trade him and start rebuilding again.