I agree with the keep it sharp guys but I also like what blub did. You should teach your kid how to use a sharp knife properly when they are young and let them use one, but until they are a little older, giving them a blunt knife that they can have with them all the time even when not suppervised is a good idea. I have similar beliefs when it comes to guns. I plan on teaching my kids how to shoot when they are young, but they won't actually get there own gun until they are older.
Teach them when they are very young, and when you are confident in there ability and level of responsibility usher them into adulthood with a real quality knife of there own.
Also, only a childs parent can judge when there child is mature enough to handle a certain responsibility, whether it be owniing a knife or a gun or just letting them cross the street by themselves. While some children mature very quickly others do not and it is the parents responsibility to decide when they are mature enough.