I think there is also a certain level of "adult-ness" that happens when one has kids. There's something about the exhaustion that puts life into perspective.
My DH and I got married and had kids much earlier than the people I grew up with. My friend did the same. I always felt we were much more on par than the rest of our schoolmates etc that we kept track of on FB who were still childless. It just seemed like a foreign concept to me, to be unmarried and childless throughout much of your 20's. Like, they had a job where they got respect, only themselves to spend their income on, they could travel when they wanted, sleep in when they wanted, take a sick day, etc. it just seems like, on a conscious level I know they had responsibilities too, and maybe they were MORE responsible than I was (maybe putting off kids until they were more financially stable) but when you're realistically only responsible for yourself, and maybe a boyfriend (or even a husband) and a cat or something, I think your whole perspective on life is different than when you have kids.
When you're a kid, your parents give you a curfew. When you're a parent, your kids give you a curfew (if you can even afford a babysitter). When you're a young, childless adult... you can go flit around for the whole weekend, if you want. Or go to the gym whenever you want. Or read a book from start to finish. Or decorate your home without wondering if the kids can hurt themselves on the furniture. Or a million other things that if you're childless, you can just *do* because you have the freedom to do so. I read in one book recently that everyone should "just take an hour every morning and do yoga" - yeah, right! Like I have an hour to myself every morning! That's a laugh.
And if it sounds like I'm jealous, heck no, I love my life the way it is. I *chose* to have a family early, and I would do it all over again. There's nothing I want more than to be in a functioning family, have twelve million kids and five dogs. I can't even quite imagine what I would do with a whole decade of me-time to myself (assuming someone plans to have kids in their 30's) and I'm sure they can't imagine how trapped I must feel (I don't).
Not to mention the stigma of having kids is huge (childfree movements, anyone?) so that sometimes takes some character-building to deal with, as well.
I don't feel that you can't be an adult without kids... I just think that it's more a significant of a change than any other transition *I've* been through. I felt "adult" at 17 (emotional/mental maturity); more adult when I moved to another city than my parents for college; more adult still when I got a grown-up job and moved in with my boyfriend (now-husband). But nothing has compared to how "adult" I feel since having kids.