I have to say, one of the things that are most mischaracterized and misunderstood about Hal Jordan is his general disdain for authority and his constant defiance of orders.
The fandom and the writers make it seem like it's something annoying that Hal does because he is arrogant and cocky, and therefore he has to be knocked down a few notches by other characters in order to learn "humility". That is not only a very unconfortable and unhealthy strategy considering Hal experiences, but it's also what would make him even more confrontational.
Hal is an instigator and a rage baiter, that's just part of who he is. But being oppositional to any command chain is not a character trait but a result of having to oppose any chain of command he interacted with in order to be free of making his own decisions.
Starting from his own family, passing through the air force and arriving at the Green Lantern Corps, Hal had to constantly not only prove himself and his abilities, but he had to defend himself, his ideals and his morals from a long line of authority figures who felt, because of the power they held over him, in the right to impose themselves on him, to make decisions and to be obeyed even against his will.
His autonomy and freedom of choice are constantly put at risk, especially when it comes to the Guardians. Famously, in the comics they are the ones who consider Hal a threat and do everything they can to control him, both with small things like giving him orders that they know he won't appreciate to enforce their power over him, and with heavy violations of his body and mind, like manipulating his memories.
Hal was often placed in positions where he had to choose whether to obey orders and maintain his own safety and that of his loved ones, or trust his principles and instincts and do what was right, even if it meant going against anyone else. Often these decisions have been forced upon him on purpose to push him to give up and submit. This has led Hal to have an instinctive, and justified, suspicion of anyone seeking to exercise authority over him.
He is a paranoid and a control freak, because he is terrified that it will be taken away from him the moment he's not keeping his guard up. Unfortunately, this, like all traumas, also manifests itself in relationships with people he considers friends or colleagues. Bruce, whose trust issues and obsession with control lead to him having a very authoritarian behavior that often toes the line of consent and uses heavy manipulation to get what he wants, is exactly the kind of person who rings alarm bells in Hal's head. Their traumas and responses to them are similar, but lead to completely different outcomes, which is what causes their difficult relationship.
Hal doesn't oppose Bruce's leadership because he's an arrogant asshole, but because until now he hasn't experienced many situations where trusting the judgment of someone outside of himself hasn't nearly led to him losing his freedom. Any attempt by Bruce (or anyone else for that matter) to push Hal to forcibly obey through humiliation, manipulation or any tactic of the sort would only lead to him fighting them even more.
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