I recently watched the movie Never Say Never which is the story of Justin Bieber's success. I must admit that I really enjoyed it and after watching it I developed theory (with the help of my wife) as to why this kid is so insanely popular.
Justin Bieber is so popular because of his wholesome, uplifting music. Every one of his songs is positive and is something that everyone can, will, or would like to relate to. His lyrics clearly value girls. How many songs on the radio talk about love without mentioning sex or being degrading to women? Not too many. He is not singing about girls, he is singing straight to the hearts of girls. Songs with lyrics like "When I smile, you smile", "One less lonely girl", "I just need somebody to love", "Your world is my world, my fight is your fight, your breath is my breath", etc... I could literally list lyrics from every single one of his songs.
Add this to the fact that he is talented (he plays the drums, guitar, and piano), young, and most would say good looking and you have the pandemic of Bieber Fever.
Thanks for keeping it classy Justin Bieber. As you mature as a musician, don't think your lyrics have to mature as well.