Writing the Tender Years

There is a trope in storytelling, and life, that says that as a child matures into an adult they think that they are somehow strange and different from everyone else. It is played off of in a hundred other tropes from self discovery to betrayal and adventure. For those formative years through the teens the character is a conflicting mass of emotions and impulses. This does have a firm grounding in reality and to write a character without it would be very odd indeed. But Why?
Perhaps it is because even the most statistically, plain Jane, character is strange during these years. That is strange to them selves. 
The infant is supremely unaware and as she/he grows into a child they slowly gain awareness of what they like, what they want, and who they are. Then, with the drop of a hormone producing gland suddenly everything is different. They feel strange. They are no longer what they were. Meanwhile they can see their peers around them behaving in perfectly statistically predictable ways. They can see the "normal" of their behavior and growth. They only thing they can't see is the equally normal feelings of strangeness that their peers are equally strongly trying to hide.  So they think that they are the only one who feels this way. 
How do you handle writing characters during this time-frame?