In terms of the business side of things, if it's true that he and his team were behind schedule and their productivity was apparently low with no foreseeable end in sight, I could probably see why Konami would make the decision to force him to market with whatever he could finish.
As for the details, I hear things got very ugly between them, which is a shame. I read in places that Kojima himself was not really too interested in making more MGS games, so regardless of what happened maybe it was for the best. I hope he's able to build a similarly interesting universe again. I will probably try Death Stranding when it comes to PC.