Maybe he believes he has a better chance to win when he isn't on LeBron's team?
Unless he developed a severe intellectual disorder, I doubt this is true.
Have you considered that maybe Kyrie made this decision based on where he feels he has a better chance to win long term, rather than putting all of his eggs into one basket?
Cleveland were a mess right now. They weren't beating Golden State, everybody knows that because they didn't even come CLOSE to beating them last season - and a Derrick Rose who has the body of a 50 year old isn't going to change that.
And if they don't beat Golden State, then Lebron probably walks after this season - just as he has done every other year when he has been on a team that has suddenly lost its ability to contend.
And if Lebron leaves Cleveland then the team is left in the hands of an amateur GM, after the much loved former GM (who did a pretty great job up until now) left the team.
So now you have a Cavs team built around Kyrie and Kevin Love, that (even after losing Lebron) is still well above the salary cap, that would no doubt make the playoffs but would have no hope of competing for a title...and a roster on which the average player age is probably 32.
Chances are that if Lebron leaves Cleveland probably goes through a full rebuild with Kyrie as the central piece - and now Kyrie has to ensure the next 3-6 years playing on a lottery bound team with no chance of winning, while playing mentor to a stream of upcoming rookies year after year.
Or he could ask to be moved to a team who actually has some kind of certainty to their future - a relatively young team that is already competitive, where he can be the #1 guy and hopefully be the man to lead that team to the finals for the next 5 years.
What teams are there in the east like that? Washington yeah, but they already have a star PG in Wall who they are highly unlikely to trade for Kyrie (a sideways move, maybe even a downgrade). You have Charlotte, they aren't bad and you have to think Kyrie is an upgrade over Kemba Walker - but other then Walker what else does Charlotte have that Cleveland would possibly want to help their future in the case of Lebron leaving? Frank Kaminsky? Not good enough. Michael Kidd Gilchrist? Too much of a liability on offense. They could probably put something together, but probably nothing that Cleveland loves.
Phoenix could offer a package based around Bledsoe, but Kyrie is not likely interested in moving to Phoenix - a garbage lottery team in the West that likely won't sniff the playoffs got half a decade.
The could try to facilitate a trade with Philly for Fultz, but Lebron doesn't want an unproven rookie PG - that's not going to convince him to stay.
Boston made sense for both team and player. Cleveland got a great haul, and Kyrie got to go to the second best team in the East - a team who (if Lebron leaves next year) could very rapidly become the BEST team in the East, while happening to also be one of the youngest teams in the NBA with only two guys (Baynes and Horford) over 30 on the roster, this is a team Kyrie can join which has a great shot at being a perennial Eastern Conference contender for the next 5+ years, which is more appealing then a Cleveland team which PROBABLY makes the finals this year, but then may very easily go full rebuilt for the next four.
This is something you have to consider. These guys aren't just looking at today, or tomorrow. They are making decisions for their future. And Kyrie's future is FAR brighter in Boston then it projected to be in Cleveland.
Then why were the Knicks a top-5 destination for him?
Ok, think about this one.
Lets say Kyrie stays in Cleveland, they lose to the Warriors, Lebron splits next year.
First things first, Cleveland is over the cap - so it cannot sign anybody. And nobody on the team beyond Kyrie really has any trade value - their next best asset is Kevin Love, and Clevleand has been trying to dangle him as trade bait for years with no success. And you have no picks of value either, since you've been dominant the past 3 years. So the first step Cleveland has to take in this rebuild process is to clear our all of their undesirable contracts, which would include (at the very least)...
* Kevin Love - $22.6M x 3 (too old to rebuild around)
* Iman Shumpert - $10.3M x 2 (bad contract)
* JR Smith - $13.8M x 3 (bad contract and too old)
* Kyle Korver - $7M x 3 (too hold for rebuild)
Those contracts add up to $56.2M which accounts for 56.7% of Cleveland's salary cap...all taken up by what are pretty much dead-weight players. Based on Boston's own experience (trying to ditch guys like Gerald Wallace and Kris Humphreys, Rondo, etc) clearing contracts isn't always especially easy, and you don't always get a lot back. So Cleveland probably has to spend the next entire season or two (or worst case, even three) trying to clear all of those contracts off their books before they can actually free up max cap space to pursue a serious free agent. So by now two years have passed, Kyrie is 27, Tristan Thompson is 28 - and finally you are ready to actually go after talent...
Now you're stuck trying to build a team around Kyrie and Tristan Thompson - both in their prime and approaching the end of their contracts. That's not exactly an all star core to try to attract free agents with. Then on top of that you are Cleveland - a city nobody wants to play for, and a franchise which has been a losing franchise every single year Lebron hasn't been there. Not exactly attractive either. So maybe it takes you two years before you finally get an All-Star to sign with you. Now Kyrie is 29. Thompson is 28 - and you're still only JUST starting to assemble your team...and Kyrie has just wasted a good 4 years of his career.
Now lets look at option #1 - trade to New York.
Because Kyrie's $7M trade kicker would have put his salary at $26M, which would have allowed the Cavs to trade him to the Knicks for Carmelo straight up, with a pick's easily thrown in as compensation.
Lebron gets his sidekick in Melo so he's happy, might be enough to convince him to stay in Cleveland for another year or two.
For Kyrie he (25 YO) gets to join Porzingis (22 YO) and Tim Hardaway Jr (25 YO) to form what is actually a pretty promising young core. Given how weak the East is, that is a team that is legitimately one big piece away from being a strong playoff team for the next 5 years - all the Knicks need to do is find that piece. Further to this, the Knicks have a pretty decent salary makeup for a young upcoming team - there is only one guy on the roster who is over 30 AND is making over $7M a year, and that is Joakhim Noah. Even his contact isn't really THAT bad, and could probably be waived easily enough using the stretch provision to bring the Knicks under the cap. And if you eventually clear cap space, then the Knicks have proven again and again that their city, their status as a big money spender and their status as a huge market team, continues to be a big attraction for free agents - as indicated by guys like Carmelo, Amare. Derrick Rose, and now Kyrie. So put a decent young team there, and it's only a matter of time before some star free agent wants to sign up and join them among the bright lights.
Is this the PERFECT scenario? No. But it's hardly a terrible one, and it's a HELL of a lot brighter then the Cleveland alternative.