"Self-supporting," I'd have to agree that is the most important thing (or at least capable of it - I'd hate to think I'm stopping being a grown-up b/c I'm going back to grad school).
Kids? What if you're 16 and living with the 'rents?
School? What you go home every weekend with your laundry?
Married? I know girls who married young and the new husband just took daddy's place.
If you can live on your own, on your own income (no subsidies from the parents!), you're an adult. Course that doesn't necessarily make you mature.
Speaking of average age for kids, I'm 26, and very few of my friends have kids. Only a very few of my friends are even married.