This one's kind of a no-brainer. Hazel, Augustus, and their friends are all teenagers who are looking for their way in life. They may be dealing with all sorts of downer illnesses, but they're still dealing with all the normal teenage preoccupations like flirting, playing with video games, and rolling their eyes at their parents.
Even though Hazel is sixteen years old and whip smart, it often seems like she's a little stunted in her social and romantic growth. But over the course of the book, she really grows into herself and experiences many of normal teenage things involved in the transition from childhood into adulthood. She learns to become a little more independent, starts being more social, and even develops a love interest. Oh, and she loses her virginity.
And if watching your boyfriend die doesn't force you to grow up, we don't know what does.