Yea they certainly can be dangerous, specially to an unknowning kid. Almost like gun safety have to learn to have absolute utmost respect for the tools you are working with and understand how to use them properly.
I never personally cut a cord, but watched it happen a few times, and with the saw only about 2' away from me lol so I was glad I still had my toes, also steel toed boots FTW.
Same here I would never let me kid grow up not knowing how to use the stuff, its great trade/skill to know and understand even if you don't ever plan on building anything.