Animals have just as much capability of fear as humans do. The difference between the animal and the human is that the human, if he or she so chooses, can embrace fear and overcome the instinctive desire to resist it. Facing fear is one of the distinctive qualities that make us human.
People can sometimes live in a very animal-like state of mind. An animal's only priority is survival. They do not care about purpose or meaning, only that their basic needs of food, water and shelter are met. Do we at times find ourselves satisfied with merely surviving as well? Are we living an animal-like existence?
We are human. To be human is to hold the image of God. We should want God-like things; we should want to model a God-like way of life. God-like living includes overcoming instinctive fear of the unknown and finding the God-given courage inside of us to do things that will ignite the growth of our soul.