A lot of you may be scoffing at this point, but I can guarantee that a number of you would think of a Disney film if asked to try to remember the first time you felt scared. Disney films have done a great thing for the development of children by introducing them to fear without going overboard and totally petrifying them. They're going to come across this emotion at some point and I'd rather be accompanied by anthropomorphic animals and catchy songs about flying (see Peter Pan or Aladdin) before I see what true fear is.
Yes not all Disney films show boat a single scene of fear, but a lot of the classics that you have seen and are most likely to show your children have a notable moment of this. Whether this is the subconscious fear of losing someone important to you (The Lion King, Bambi, Dumbo to name a few), the fear of being abandoned or becoming an outsider (Toy Story, The Hunchback of Notre Dame) or being just all around genuinely terrifying, ranging from the Evil Queen's haunting transformation into the Witch in Snow White to the eerily possessive nature of Mother Gothel in Tangled. Fear has been almost omnipresent in the Disney catalogue.
It's a fact of life that we are going to be scared in life, and I for one am happy that my first encounter with fear was through a Disney film (it was Dumbo) than it being at the hands of a person in the real world. It is important for children to learn about fear at a young age so that the real world, which is a scary place, doesn't seem as scary.