Dirt bikes are not dangerous, but they are evil and mischievous... They will sneak out of the garage at night and leave tracks all over the neighbor's yard, track mud into the house, and constantly drink all the gasoline you leave in cans in the garage. HAHAHA
Seriously, though... they are not dangerous, otherwise millions of them would not be sold around the world! What is dangerous are DANGEROUS BEHAVIORS, like trying to jump over the house with them. Use them for what they are intended... transportation (and fun) in the dirt, fields, and trails! Keep your speeds to what you can handle, wear protective gear (helmet, gloves, jacket w/armor, kneepads, and sturdy boots. As you learn more skill on that 70cc, you'll eventually want to upgrade to a 110, 150, 250, 450, or maybe even a street-bike!
Your parents are horribly misinformed or just way overprotective. Prove them wrong by being a responsible person and learn to ride responsibly (and of course have fun doing it).
Riding and repairing motorcycles for 40-yrs (started on dirt bikes when I was 6)