I think we've established that David's murder gives Kirk sufficient reason to distrust Klingons. It doesn't help that they keep proving him right, coming after him time after time.
But even in those cases, the Klingons who were after him were rogue elements acting out of turn with respect to the rest of their government. Kruge, Klaa, and Chang were all renegades of some sort (though Klaa's behavior stemmed from immaturity and a desire to make a name for himself rather than blatant disregard for the law): Chang was a traitor, and Kruge was just nuts. Their behavior wasn't representative of the entire species.
I suppose one could argue that the High Council's inability to control the military suggests an inherent lack of discipline among Klingons as a people, but that doesn't warrant calling them animals. The Federation had its own problems with rogue elements stirring up trouble, even during Kirk's time. Were men like Cartwright or Colonel West animals because they decided to circumvent the law to ferment war with the Klingons? Was Valeris an animal because she helped them? I don't think characterizing any of the parties involved that way is fair. They were misguided and inflexible, but that's a long way from being savage.