I've read that Azog swore an allegiance to Sauron to destroy the line of Durin. Which implies that Sauron was the one who wanted the Durin line wiped out. Like it was some part of a larger plan to regain control of Middle-earth. However I have also read that during the battle, Azog swore an oath to his forebears to wipe out the line of Durin. In both cases it would be before Thorin cuts off Azog's arm. And the movie makes it seems as if Azog is hunting Thorin out of revenge for disabling him. So why exactly is Azog sworn to wipe out the line of Durin?
I want to know the explanation for the Peter Jackson movies, not the book.
I have more information, but still my question is not answered. In the "Desolation of Smaug" Bolg tells Azog: “They are gathering at Dol Guldur. The master has summoned you.” Azog then goes to see his master "The Necromancer" (Sauron) and The Necromancer appoints Azog to lead his armies. Azog asks “What about Oakenshield?” because it seems he's only really in it to kill Thorin who disabled him. The Necromancer replies that “War is coming,” implying that they have other priorities. Azog gets very angry and says “You promised me his head!” And even more angrily the Necromancer replies “all will die,” implying that Azog shouldn’t worry. He’ll have Thorin’s head by the end of it.
So this new information definitely supports my idea above that Azog really only cares about killing Thorin for revenge due to his arm being cut off. But Thorin cuts off Azog's arm near the very end of the battle. And Azog began the battle sworn to wipe out the Durin line. That's why one of Azog's first acts in the battle is to behead Thror. And Thorin really only goes after Azog & cuts off his arm in retaliation.
- I have even more information. I went back to "An Unexpected Journey" and watched Balin tell Bilbo the story of the Battle at Moria. His quote is: "We went to reclaim Moria, but our enemy had gotten there first. Moria had been taken by legions of Orcs. Led by Azog the Defiler, a giant Gundabad Orc who had sworn to wipe out the line of Durin. He began by beheading the King (Thror)." So we know for a fact that Azog went into the battle already sworn to wipe the line of Durin.
So why is he sworn to wipe them out?