Actually, this is normal in being human, and most living things do worry about being safe. What can make it more challenging is that when something does happen that traumatizes us, we become even more concerned about our safety. PTSD is a condition that magnifies the our fears, and this is what can become a challenge for a person depending on their personal history where they may have grown up in an environment where they never found a true sense of safety and formed a more confident personal sense of identity and developed a sense of confidence in "self".

The other things about questioning one's sense of safety that is normal is that it's the driving force within our humanity that led to our becoming more nomadic in search of food and safety which contributed to how we gradually inhabited many different contenents on our planet.