This is the way to interpret dream of running away from animals. In the dream, when you ran away from animals, it shows you’re insincere in befriending them. You maybe running away from your animal instincts, which are actually your natural instincts. After having this dream, you should reflect on what you had been doing which made you decide to escape certain aspects of your personality.
How long can you keep on running away from your natural instincts? Maybe its time to face your fears and manage the situation.