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So far I have not found any news that says why Nistelrooy was fired other than because Amorim already has his own coaching staff. And I think it is reasonable because Nistelrooy will not get the same place because Amorim also has someone in Nistelrooy's position when he was with Ten Hag. Actually Nistelrooy has also said that he does not want to be a permanent coach. But the positive results that United got when Nistelrooy was a temporary caretaker could make some people have high expectations for Amorim. People will compare United's performance in the first few games. But I agree as @punk.zink said, a coach needs 1 or 2 seasons to create an ideal team. It is very difficult to get success in the first season.
Manchester United asked Van Nistelrooy to be an interim for a few games. It's until they were finalized a deal for a new coach, Amorim. He has a contract with United just for 4 games, then he stepped down as an interim because his contract ended.
There's no need to fire him because how long he coached the club has been mentioned on his contract.