When Balin was recounting what happened in Moria, (i.e. the flashback), he stated that Azog had previously swore to put an end to the line of Durin (Thorin and his predecessors), which is why Azog cut off Thror’s head. Azog loses his arm AFTER this, meaning that the loss of his arm wasn’t his initial motivation for hunting down Durin’s folk. The loss of his arm is simplyafew more sticks on the fire that is his hatred for Thorin’s people. The origin of this hatred is never explained. This is what the reviewer is addressing.