I have seen this topic being bounced around on social media, that the big philosophical difference between KM and Big Mike was the option routes.
Most of Dak's actual ints (not picks where the ball hit the WR in the hands and bounced off), but actual picks were misreads on option routes. The WR reads the coverage one way and Dak reads it another way or the WR runs the route wrong by going behind the safety instead of crossing his face. Almost all of Dak's picks in the middle of the field this year were misreads on option routes, see Green Bay game as a perfect example.
The Garrett/KM offense uses a lot of option routes whereas Big Mike is more of a West Coast guy that uses very little option routes and instead focuses on short, quick passes and RAC yards. Most the routes are predetermined and dont change based on coverage, but the coverage dictates where the ball goes. Philosophically speaking, using more West Coast plays with fewer option routes seems like it would be a big benefit to Dak, especially if he and the WRs are just not reading the coverage the same.
Maybe Big Mike wanted to change the offense to use a lot fewer option routes and KM disagreed since a large portion of his playbook is based on using option routes throughout the entire route tree.
So, I dont know if I believe this 100% that this was the main area of friction between KM and Big Mike but I thought it would be interesting to see what you guys think.