You can become a paramedic in 1-2 years, why does it take that long to learn how to safely cut and dye hair?
For the very reasion you stated. Safety. Do you really want someone hacking away at your hair with a sharp pair of scissors? You have ears, don't you? And that doesn't get into the issue of HOW to cut hair so it looks decent. How do you properly cut a bob? Layering? What do you do with different types of hair (straight, curly, African American, thick, thin, etc)? How do you cut a man's hair compared to a woman (not every guy gets a buzzcut)?
And those chemicals used to dye hair can cause burns to the scalp (and skin if spilled) if not properly applied. Do you want your pre-teen daughter wailing in your ear for weeks and months that her head burns and now she can't have good looking hair because the colorists burned her?
I know it seems silly to have to go through all of this, but there are valid reasons to be certified/licensed/whatever. This also gives you legal rights if something goes wrong.