I agree, it takes a while to reach the point when your knife becomes an extension of your arm. I never really thought about that myself, growing up with a SAK and puuko since I was 7 or so. But looking at a lot of my friends and camping buddies I can also see that most urban dwellers nowadays aren't used to handling a knife safely and effectively. Which is a shame considering it's one of man's oldest tools.
As for knife safety, it's all about common sense. Never cut toward yourself, always keep the edge sharp, don't let any fingers get in the way and you'll be fine. Whittling sticks and carving wood when you have some spare time is excellent practice and will teach you almost all skills you'll need. Larger chopping blades or machetes are more dangerous but still entirely safe as long as you follow a few obvious precautions.