The important point (for me) is that we have an innate tendency, for evolutionary reasons as you very well mention, to protect us in excess. However, human beings have an advantage over other animals and is that we have developed a spectacular degree of consciousness, especially awareness of our own existence (The self). This same awareness we can use it to "speak to ourselves" and make us understand that almost always the fear we feel is not proportional to the potential risks, is in reality an illusion or a half-truth.