Brody's arc isn't getting over his fear of the water. Give him (and Spielberg) a bit of credit. His character is far deeper than that. The film isn't really even about a shark, it's about a guy finding his way in a new world that he isn't really at home in. He's afraid of the water and lives on an island - it's your classic fish out of water set up.
Outwardly Brody likes Amity, "Here, one man can make a difference" but he knows he's not particularly happy because he's both demanded and rejected at the same time. The locals badger him for every little thing but they think he's a sissy. He lives in Amity but he and his family will "never be islanders." He's the chief of police but the mayor countermands him at every turn and yet he's the one that gets slapped in the face by a grieving mother when her son dies.
He's a guy being pulled in every direction and he has no idea of how to be all things to everyone or where he really belongs. Most importantly, his family, who he moved for a better life is also worn down by the island - his son is attacked by the shark, his wife grows distant the more he tries to face up to his official responsibilities and by the time he goes out to sea, she is in tears and he's facing a very uncertain future.
Brody really wants to make a go of it in Amity but when the shark comes along, (which is really just a metaphor for the violence and bloodshed he ran away from in New York) he is forced to confront something that threatens to stop him from finding his place and settling down. He has to stop running and become what he believes he needs to be in order to get his life back on track, whatever the cost, whatever he has to do, whether it's going out to sea despite hating the water, looking like a bumpkin in comparison to Hooper and Quint or telling the mayor what needs to be heard - "You're gonna sign it, Larry. You're gonna sign it so I hire Quint to kill the shark," - would he have dared say that to the mayor at the beginning of the film? No. This is a man that is changing and by the end of the film, once he has personally destroyed the threat, after everyone else has failed and he's paddling back to shore, we are left with the distinct impression that once he gets back, things will have changed.
In summary; a scared man gets brave - exactly what you said - but that fear and bravery runs far deeper and more abstractly than you seem to realise.
And I won't belabour it but Indy's arc has nothing whatsoever to do with getting over a fear of snakes. It's about him realising he wants Marion more than the ark - that he wants love more than trinkets.
He initially seeks Marion out for an object, a thing, and discovers she has become something of an object herself. Soon after, he is forced into a partnership he doesn't want. Then, throughout the course of the film, he chases both Marion and the ark but it seems quite clear he values the ark more - tying up Marion in the tent rather than simply escaping with her, for example. But then it starts to get a little fuzzy. When he swims over to the submarine that has taken both the ark and Marion, we're left wondering who is he chasing now? We are soon left with no doubt as Indy threatens to blow up the ark with a bazooka - "All I want is there girl," - and finally, if there were any doubt left, despite his bad meeting with the government types at the end, he still chooses to walk away from the ark and leave with Marion. This is a guy who has discovered there is a greater reward is saving the people he loves over the relics that don't love him back.
I haven't seen DaVinci Code but saying it has a Spielberg connection and therefore a bogus character arc seems like bogus reasoning. I'm sure there's more at play in that film (however bad it is) than a simple case of conquering claustrophobia.
I'd just like to weigh in on a couple of points on the subject of Jaws.
First -- and perhaps the biggest point.
Stephen Spielberg is a very talented fellow. But he is a talented *director.*
He did not write Jaws. He didn't write the book and he didn't write the screenplay. The screenplay was written by Peter Benchley and Carl Gottlieb. The "Indianapolis" monologue was written by Howard Sackler, John Milius and re-written by Robert Shaw.
I can't tell you how much it bugs me when people talk about, "Well Spielberg shaped the character arc to be this, that, and the other thing" -- No -- the *writer* did. The writer of the screenplay, who created the characters, who invented the scenes, who wrote the dialogue -- he is the one who created the character arc (such as it is).
Not the Director.
This is a kind of lazy shorthand that critics use, wrongly, all the time. I just hate to see it being used here, on a screenwriting newsgroup.
Second, regarding Brody's character arc -- which, of course, has to do with the larger theme of this story.
This is a story that is, thematically, about redemption. Brody is someone who has fled from the big city to a small town, to escape from the dangers and responsibilities of that world -- and where does he find himself? What does that fear of water signify?
He comes here to escape the hard moral choices that come with being a cop in a big city - life and death choices. That is what he fears -- and instead, finds himself morally and thus, thematically, "in over his head."
And what happens? When presented with the first tough choice as Sheriff -- he balks. He makes the wrong the choice. Everything tells him that a shark has killed the girl in the opening scene. He knows it's a shark. He doesn't change his mind because he thinks it isn't. He changes his mind because he's pressured by the Mayor and his cronies. He goes along so as to not make waves.
And what is the result? An innocent boy is killed. The hard choices he tried to escape -- the "waters" that he feared, he now finds himself swimming in. He couldn't escape them after all. And he's failed, disastrously. And he keeps floundering, keeps trying *not* to swim -- let others fix it, the coast guard, the Marine Biologist Expert, anyone but him, and what's the result? There is yet another death, and his own son is almost killed.
And finally, he realizes that there is only one choice. There is no escape. In order to redeem himself, he is going to have to take full moral responsibity -- it can't be passed on to anyone else. He has to close the beaches. He has to get the boat -- and he has to be the one to go out into those waters and risk everything -- his own life -- to make it right.
And when he has finally made it right -- when he has embraced the full moral responsibility that he had been ducking all along -- then he is, symbolically, "no longer afraid of the water."
That is what Jaws is about.
(And the Da Vinci Code is just a complete piece of crap that isn't even worth thinking about).
NMS