I agree with most of what's been said, but honestly I find what's been stated as the differences between adults and 16ish year olds a bit too idealistic. I know too many adults that don't possess all or even a few of those characteristics.
As far as black belts and teaching, not all black belts can nor should teach. A lot of adults just don't possess that quality. I agree that a 1st dan should be able to work with a colored belt student or two individually to help them polish up technique or walk and talk them through stuff, but there's a huge difference between running a class for an hour or two and helping a lower ranked student out. There are several 2nd-4th dans I train with that are excellent karateka and no one would question their rank that don't teach because they wouldn't be very good teachers. They're very good at helping people like me when I ask (and even when I don't ask), but they wouldn't run a full class very effectively. Just throwing them the keys and saying "see you next week" wouldn't be the best choice my CI could make. They wouldn't do anything inappropriate by any means, but class would be awful. I do think however that if someone is at or near master level, they must be able to effectively teach and run their own dojo. Not from a running a business standpoint, but purely from a teaching standpoint.
Would I have been ready to be a black belt at 16 or 12 or younger if I was training back then (assuming this wasn't some black belt mill)? If my hypothetical teacher thought so, then yes. My rank is my rank; my name is (or was when I was a black belt) on my belt for a reason - it's mine. I know what I put into it. I defined my rank, it didn't define me. If an unworthy schmuck standing next to me in class has a few more stripes on his or her's, it doesn't downgrade mine. If someone with far more skill and knowledge had less stripes on their's, it doesn't make mine any better.
@Buka i really like your standard of having to defend against a full grown man. Knowing your track record here, I'm pretty confident that that was one of many prerequisites. Not that I'm saying you're wrong by any means, but what about someone who all the training in the world won't get them to be able to defend against a full grown black belt man? Would a 4'10 85 lb woman who trained hard day in and day out, and could easily hold her own against any average sized woman with respectable skill not be worthy of a black belt if she couldn't fully defend against the 5'10 185 lb guys? What about a 4'10 100 lb guy who could go toe to toe with any guy up to 6" taller and 50 lb heavier? I'm most likely wrong in my assumption, but it seems like some people have nearly no chance.
@FlamingJulian - if your teacher thinks you're ready, you're ready. Go earn it!