I'll try to summarize today's Athletic article for those w/o a subscription...
According to the Athletic, whose sources are almost certainly United employees so take with a grain of salt, Wilcox and Amorim had a meeting on Friday at the end of which, after a "massive fallout", Amorim said he wanted to leave the club and that he'd be contacting his agent. If that's true, they should have fired him right then and there. Doesn't sound like he even went to speak to the players. He just went straight to his office, packed up his things, and left. Poor from him, but I guess it's fitting of a guy who's quite emotional and honest to a fault.
As has been reported, it came down to player acquisitions (or lack thereof) and the hierarchy wishing to see a transition to a 4 man backline.
In regards to transfers, it was a culmination of getting Lammens, Mbeumo, and Sesko instead of Martinez, Semenyo, and Watkins, not getting Semenyo in this window (Amorim apparently really likes Semenyo), and not getting "more players" that he needs.
In regards to tactics, Ratcliffe started pushing for a 4 man backline. Wilcox preferred it but largely left the decision to Amorim until more recently pushing for it. Amorim got fed up with it.
Personally, I think Amorim has no leg to stand on in regards to transfers. I get frustration at being told Semenyo is too expensive and then seeing Mbeumo come in for virtually the same fee. But Ratcliffe and co made pretty clear from day one that they were going to have a large say in transfers. And besides, Lammens has proven to be an excellent piece of business and Mbeumo is almost certainly our 2nd most important attacking player.
But United effed this in regards to the tactical disagreement. Maybe they thought they could Jedi mind trick Amorim into slowly transitioning to a 4 man backline but if that was their plan, it's a pretty horrible one. Can't blame Amorim for his 3 man backline. He said since before Day 1 that was his tactic. And if Ratcliffe's tactical opinions are having even miniscule influence at the club, then we are well and truly screwed.