I've been thinking about this, and my thoughts so far are... a 5/6/7/8-year-old is, I think, still doing a lot of learning by copying their parents and peers, so introducing knives and knife safety at this age is a good idea since they will copy you without thinking much about it, and sensible knife handling will become ingrained, and they will take your attitude to knives, which is hopefully that they are tools only. Also, kids that age will spend almost all their time either close to or with an adult or two, so that if something bad happens, there is no time lost in finding out and doing something about it. Not only that, but when they are still young they are much more likely to scream or seek help from an adult than a teenager is.
And you say "even teenagers do silly things", well hell, even adults do silly things. There are several threads on these forums alone that testify to that, and we all like to think we know what we're doing. In my (very limited) experience, kids are far more likely to seek help for stupid injuries than teenagers or adults.
I think it boils down to - do you want your kids to cut themselves for the first time when you are likely to be nearby to sort them out, or when they're on their own and trying to be independent of you.