It's odd seeing how many of you are putting the blame directly at Kohli and not even some of it on Kumble. Yeah, we are winning but if the players aren't happy being coached by a drill sergeant, they're going to speak up about it and all the articles I have seen (Cricinfo comes to mind) explicitly mention it's not just Kohli but that a lot of the players didn't appreciate his man management skills.
It is not Kohli vs Kumble, it's players vs Kumble and in every scenario I'm going to side with the players because they're the ones who actually impact the game.
The players can't have any say on the coach. And ultimately if you see the results under Kumble, it has been almost spotless (except for a minor distraction here and there, and this includes the CT 2017 final that we just lost; also before this final started, the rift between coach and captain was made public and so it puts a doubt as to how involved the players were in ensuring that the coach goes). When someone pushes you to give your best, you go and complain that "this guy is pushing me too much; I don't want him in the side anymore?". How ridiculous that sounds? There can be no passengers in this team who are not willing to step out of their comfort zones.
You obviously got to be a hard taskmaster when you coach an international side and that too a side like India who are constantly under the media glare 200%. India is the most controversial side in the world cricket and a side that has every eyeball trained on them, many waiting to pounce on them and laugh if they fail. For long, we have wanted to match the standards of the top non-Asian sides in the world in terms of fitness, bowling standards, batting standards, etc. All of this was coming into place under Kumble's coaching. Kumble has not done anything wrong like leaking things to media (that rumor about him circulating info about players on WhatsApp is very likely a rumor as no reliable source posted that info). It's so clear that India were progressing in the right direction under Kumble and clearly looked ready to take on their biggest challenges (winning overseas in test series). This is a big setback on us, and I am going to be siding by Kumble and I despise the way in which Kohli played his hand in this entire affair.
And seeing the way Kumble saga turned out, there is no hope in hell of Rahul Dravid coaching India in the near future.