Q: Why do children have fear?
Because they are weak.
Physically they are weaker than the grown-ups around them and, generally, they are also weaker vitally and mentally.
Fear stems from a sense of inferiority.
However, there is a way to be free from it: it is to have faith in the Divine Grace and to rely on It to protect you in all circumstances.
The more you grow up, the more will you get over your fear if you let the contact with your soul develop in you that is to say, with the truth of your being and if you always strive that all you think, all you speak, all you do should be more and more the expression of this deep truth.
When you will consciously live in it, you will fear nothing any longer, in any domain of your being, because you will be united with the universal Truth which governs the world.
Ref: On Education