Good relationship between the manager of a club and the owners helps the team to be together, a divided house can not flourish, when the manager is not in a good terms with the management the whole situation may affect the performance of the club entirely because the manager may not be concentrating in his coaching jobs and players also may not have the zeal to give their best in the football pitch in so doing politics may be introduced in a way that individual players may decide whom to support or take instructions from as the ugly situation is going on either the club owner or the coach and this may lead to underperformance of the football club.
No matter how good you are as a manager in as much as you were hired by a person or group of persons, you are answerable to them because there are conditions and reasons that made them to hire you as such you don't act on your own, although many managers has used their coaching strategy to bring success to a club and thats the purpose for their employment but before you make any step as a manager, you must involve the owners of the club before anything although sometimes club owners are very annoying in terms of decision making.
As for morinho we know that he is not a bad manager but he is arrogant although am not judging him because different people has their personal character but I believe that what happened may be as a result of his attitude and nothing else.
People think that being a good manager only means getting good results, but that is not the case at all. Plenty of good managers who got results still got sacked, biggest example would be Napoli firing their champion manager just recently, did much worse after he left, and yet still sacked him.
Mourinho or anyone else, if you are a jerk to owners or the other office management team, then you are going to end up with trouble. Directors are there for a reason, and if you are a jerk to them then you are going to end up with a bad result. Mourinho realized too late in his life (probably right about now) that he needs to listen to the owners and presidents of clubs to keep his job, even a cup may not protect his job, he has to do better.
In many cases, even if the manager is right, the club owner is never wrong. Most managers are fired because they want to have a greater influence in the team, in terms of player transfers, long-term plans and so on, which are very likely not liked by the club owner. The number of trophies presented will be a consideration, but differences in vision with the club owner are a disaster in a manager career, Jose Mourinho is a very relevant case where his relationship with the club president often ends badly.
For now, only a few managers have stayed at one club for a long time, maybe one of them is Pep Guardiola, we can see that he is very rarely or almost never heard of having a conflict with the club owner in any way. Aurelio De Laurentiis is probably one of the most arrogant club owners at the moment, he does not seem to regret his decision to fire Spalletti. In the Premier League, before Todd Boehly acquired Chelsea, Roman Abramovich was another example. Sometimes many club owners are only oriented towards results, impatient in the process, and only want to see their team always successful, something that not every manager is able to fulfill every season.