"I don't know what to tell you, laddie. Sometimes wise and powerful wizards just throw the occasional bitch-fit, I guess."
The Book: As it's starting to rain, Bilbo begins to complain about how much he misses his home, by the fire with a cup of tea. By night time, as Thorin begins to ponder what they Company is going to do about food and a place to eat, the dwarves notice that Gandalf is missing. Though Dori and Nori complain that a wizard would be nice to have to help with the rain, they don't think anything of it; Gandalf never said if he was with them for the entirety of the adventure, or if he was just keeping them company for a short while.
What difference does it make? This is not an enormous difference. What matters is that, for a short while, Gandalf disappears. It isn't entirely important if it's due to a disagreement with Thorin, or if he simply has his own reasons. However, Gandalf doesn't need a reason for leaving; it's just his way. Gandalf's mysterious ways are part of his allure and charm as a character. Manufacturing reasons for his behavior belies that.
My Opinion: I didn't like the argument between Thorin and Gandalf, for two reasons. One, obviously, I found it to be an unnecessary departure from the character in the book. When Gandalf disappears, you get the feeling that he's up to something - perhaps related to the quest for Erebor, or perhaps not. The mystery is what matters, and leaving it ambiguous kind of hints at a greater character, with a greater purpose. Maybe Gandalf is involved in several little quests, and likes to pop in and out of them at his whim. Or maybe it's just in his nature to come and go as he please. Watching him get all pissy and storm away because Thorin's being stubborn, though, just makes him look petty.
Thorin's attitude is another thing here that I didn't like. Specifically, his attitude towards Elrond and his ilk. Thorin is resentful towards Thranduil, who did not help the dwarves when doom came to Erebor. Transferring this anger towards Elrond is literally racism. Elrond is Lord of Rivendell, and Thranduil is King of the Woodland Realms. Not only are these places hundreds of miles apart, but they have entirely different cultures and even different types of elves living there! (Noldor elves in Rivendell, and Silvan elves in the Woodland Realms, if you're interested) Don't get me wrong, I don't actually mind that Thorin is portrayed here as a bonafide anti-elf racist. It makes for an interesting character. I do mind that his racism goes by unaddressed. That was the perfect opportunity to give Gandalf a reason to storm off! To an audience that might not know the difference in elves, it just looked like Gandalf overreacted to Thorin's simmering resentment. Have Gandalf angrily declare that "Elrond is not Thranduil," or "Not all elves are the same, Thorin Oakenshield!" If you insist on having an argument drive Gandalf away, might as well have it be about the leader's unreasonable hatred of an entire race.
To be fair, they do all look the same.