Listening to SJ he mentioned MM brought up moving on from Moore. At least it sounded that way.
I don't remember the precise quote, but someone in management said something like "McCarthy made the case to make him the play caller". Basically that he pushed Moore out.
Likely it was more a step for self-preservation than a desire for himself. It wasn't the defense that failed in the playoffs, it was the offense. Some head was gonna roll. Unfortunately, we're already locked into Dak. So a change was either McCarthy or Moore.
Management:
You're the HC and we failed in the playoffs, and we failed in what is supposed to be your area of expertise, the offense.
The natural counter from McCarthy would be:
I wasn't the one calling the plays. I can coach and direct as much as I want, but Moore just has a different philosophy than mine, and while I agreed with keeping Moore as OC, you made it a condition of taking the job. If I had picked an OC myself, it obviously would have been someone closer to my philosophy.
So Moore is out, and even before we get a new OC, the decision is announced that McCarthy will be the play caller going forward. If it were *just* dissatisfaction with Moore that prompted his firing, it's more natural to leave the play caller decision to *after* you find a new OC.
I think McCarthy threw Moore to the wolves to keep his tenure alive. Leaves McCarthy battling with Dak to survive the next failure, but that largely comes down to whether management leaves themselves the option of dumping Dak if he isn't cutting it.