Fear is such a little, inconspicuous word, known to everyone. It can completely take over your mind and push you to things you don't want to do at all.
Fear is something everyone once felt. Even if do not want to feel it, you will feel it anyway. It is not about thinking that something is scary, you just suddenly sense this creepy emotion, flowing out all of your body. You don't think that you are scared at the very moment. Thoughts just split into your mind making it impossible for you to think about nothing else but the object, which caused fear to you. You can't fight with your instincts. With the essence of your existence.
There's also a different type of fear. Camouflaged, attacking suddenly, but remaining for a long period of time. If you dread something and you are forced to be exposed to that, you will do many things just not to interfere with the thing, which made you frightened.
It is possible to fear almost everything and young children do that actually. Why? Humans, although more intelligent, are still just animals. Hence, they tend to fear everything unknown to them. It is not something unusual. It's just an instinct that helps to survive living beings. The philosophy is like that; if you are not sure what's that, you'd better run away so that nothing will happen to you. Simple like that. For us, though, it's not that helpful. Living in such diverse world, where knowing is black or white, we shouldn't fear everything we don't know. By learning and exploring word, we are taught that there are things to fear as well as there are things to not. However, it doesn't work always so people still are scared because of things they shouldn't be afraid of, just because they're not sure what those things actually are.
Is it likely to overcome fear? Yes, we do that for the whole life. Without it, we wouldn't be able to go out of the house. Just by exploring and learning we learn what is to be scary, and what is not be afraid of. It is what also for example dogs do. When they meet for example new human, they keep distance and they often bark rather than being happy. What is crucial, though, is that they sniff that person to find out if they can trust new person. People do something pretty similar, although they're not aware of that.
So, should we be afraid of fear? The answer is ambiguous. I'd say, that being aware of fear's existence in our life is far better than fearing it itself. We should also know when we are scared, which is, surprisingly, not that easy. It'll be easier to overcome our own fear, when we'll know how it works and that is a normal, inherent part of life.