In The Hobbit, it is made out to be that Thorin is after the gold but really he is after the Arkenstone.
Why did the director want him going after the gold rather than the Arkenstone, and tried to sell the idea of his perpetual lust for gold even though he only wants the Arkenstone which was rightfully his?
I think you mischaracterize Thorin; yes, the Arkenstone was of supreme importance to him, but that doesn't mean he didn't want the gold too.
In fact, this isn't wholly an invention of Peter Jackson; Tolkien discussed the same idea, though less dramatically1:
Long hours in the past days Thorin had spent in the treasury, and the lust of it was heavy on him. Though he had hunted chiefly for the Arkenstone, yet he had an eye for many another wonderful thing that was lying there, about which were wound old memories of the labours and the sorrows of his race.
The Hobbit Chapter 15: "The Gathering of the Clouds"
[C]urb your pride and your greed, or you will fall at the end of whatever path you take, though your hands be full of gold.
Unfinished Tales Part 3: The Third Age Chapter III: "The Quest of Erebor"
Jackson holds that Thorin was overcome by a curse on the gold2, which overrode his good sense and ultimately leads to his downfall; this isn't an uncommon reading, and John Rateliff, author of The History of the Hobbit, is one prominent scholar who supports it:
That Jackson’s Thorin suffers from dragon sickness "is an unusual reading of the it, but one that I advocated for in The History of the Hobbit," Rateliff says. "I was very interested to see that they'd arrived at the same conclusion."
Narratively, this drives one of the major conflicts of the film: other people (Bard and the people of Lake-town, centrally) want Thorin's gold, but Thorin won't give it to them:
Bilbo: [Y]ou made a promise to the people of Lake-town. Is this treasure truly worth more than your honour? Our honour, Thorin, I was also there; I gave my word.
Thorin: For that, I am grateful. It was nobly done, but the treasure does not belong to the people of Lake-town. This gold is ours, and ours alone. By my life, I will not part with a single coin.
The Hobbit: The Battle of the Five Armies (2014)
1 A sentence which rather sums up the entire trilogy, actually
2 There's also basis for this in Tolkien's lore, which I discuss at Is "Dragon Sickness" a figurative or literal curse?
Thorin wanted to regain everything that Smaug had taken from his family. The Arkenstone was indeed the most precious object in the hoard of treasure that Smaug stole from them. It is true that Thorin valued it so highly that he could not (until the end) forgive Bilbo for taking it to trade for peace, but I don't think that means he wan't interested in the gold or the rest of the treasure.
However, it seems clear that what he (and Gandalf) really wanted to achieve was to eliminate Smaug and have the dwarves retake Erebor to establish an area in the north that could resist Sauron in the coming war.
‘I grieved at the fall of Thorin,’ said Gandalf; ‘and now we hear that Dáin has fallen, fighting in Dale again, even while we fought here. I should call that a heavy loss, if it was not a wonder rather that in his great age he could still wield his axe as mightily as they say that he did, standing over the body of King Brand before the Gate of Erebor until the darkness fell.
Yet things might have gone far otherwise and far worse. When you think of the great Battle of the Pelennor, do not forget the battles in Dale and the valour of Durin's folk. Think of what might have been. Dragon-fire and savage swords in Eriador, night in Rivendell. There might be no Queen in Gondor. We might have returned home from victory here only to ruin and ash. But that has been averted - because I met Thorin Oakenshield one evening on the edge of spring in Bree. A chance-meeting, as we say in Middle-earth.
The Lord of the Rings: Appendix A
