The Tech Report came across an interview with John Carmack that reveals he didn't leave id Software on best terms. In November the official statement said Carmack wanted to concentrate on his new role as CTO of virtual reality firm Oculus, but it appears that the real reason he left id is because ZeniMax, id's parent firm, refused to partner with Oculus. Carmack also revealed that he's no longer a technical advisor to id as "it just didn't work out" for him.
According to a USA Today story spotted by The Verge, Carmack wanted ZeniMax, id Software's parent firm, to partner with Oculus so that Wolfenstein: The New Order and Doom 4 would support Oculus' VR headset. ZeniMax, however, wasn't interested. From the USA Today piece:
[If the deal had gone through,] Carmack would not have left id in November and would have continued working at both companies. "I would have been content probably staying there working with the people and technology that I know and the work we were doing," he says.
"But they couldn't come together on that which made me really sad. It was just unfortunate," Carmack says. "When it became clear that I wasn't going to have the opportunity to do any work on VR while at id software, I decided to not renew my contract."