Probably the first time I came face to face with intense fear when I was in 2nd grade, at KV Hebbal, my school in Bangalore.
Painfully shy and introverted, I was terrified of talking to anyone. One day, when it was the turn of our class to read the 'Thought for the day' in the assembly, the class teacher randomly picked me as part of the rotation.
I did not think I would survive speaking in front of 1,000 plus students. I don't know what I said but I blurted something in the mike. But surprisingly, after that incident, my fear of public speaking came down a fair bit.
In fact, conventional wisdom says that to overcome fear, you have to face it head-on. It turns out that recent neuroscience research also supports this idea.
Our brain forms emotional memories, associating any situation with fear (e.g., public speaking with fear of ridicule). The only way to rewrite that memory association is to experience the situation but not have a negative outcome (e.g., give a public speech which goes well). In fact, even PTSD can be treated this way. (Do check out videos on brain plasticity on Amazon Prime).
In summary, fears are just emotional memories we can break by facing and falsifying them. That is why kids need to be exposed to the world outside textbooks.