I don't becoming an adult is really about you, exactly. It's not about your independence, or your actions.
It's about when other people become dependent on you.
I think this is the way that it has long been thought of in cultures outside of the post-Enlightenment West. This was my strong opinion after reading Dostoyevsky, Tolstoy, (Russia isn't western like the rest of Europe) and Aquinas, Augustine, and Aristotle. I think that this is in part what the Apostle Paul is saying in 1 Corinithians 13:11 ( http://www.esvbible.org/1+Corinthians+13%3A11/ ), where you'll note that he doesn't say the equivalent of stopping to be like a child meant I had become a man, but rather I became a man, so I stopped being like a child.
I think about soldiers I have met and know. They change when they get to NCO status. I think of the boys I have met from North Omaha, which is arguably one of the worst places in America for young African American males, and that there is a difference between the ones who are the oldest in their families and the ones who are the youngest, even if they are the same age. And I think of my friends, and how we've changed when we've had kids, or when someone started a business and got ( real, not just one of his buddies-while-still-in-high-school ) employees.
Adulthood isn't about you, it's about your relationship to others.