Don't you remember being that age? Even without ascribing personal traits like arrogance, its just hard to have had enough experience to understand the potential depths of your ignorance.
Reminds me of one of my favorite quotes, attributed to Twain but surely not -
"When I was a boy of fourteen, my father was so ignorant I could hardly stand to have the old man around. But when I got to be twenty-one, I was astonished at how much he had learned in seven years."
Where does the confidence to make such an assertion come from? Simply by virtue of being a teenager yourself?