If Dementors represent the phenomenon of depression, then hippogriffs symbolize the universal demand to respect living things. The only requirement of a hippogriff is that you bow before it and treat it well in order to gain its trust; Harry does so easily because he is careful around people and things that are careful with him; Malfoy fails to win Buckbeak's trust because he insults the beast. Instead of being quietly left alone, Malfoy was attacked. There is an all or nothing principle at stake here, in which the presence of basic respect can win you everything, likewise the absence can badly hurt you. Finally McGonagall's lesson on animagi foreshadows later events in the story. The dual nature of animagi parallels the dual nature of most things in this story, and in this series in general: the duality of identity, of sides to the world (Muggle and Magic), of time and predictions, and of ways of viewing events.
