I think your parents and you, do not know enough about the dangers of cycling. They are overly scared and you are not scared enough. Take the advice given above about listening to and talking to your parents.
Get your ducks (information) in a row before you respond to their concerns. If you can not bring them around, then when you are old enough and financially capable to support yourself, you can do as you please... but as long as you live in their home and they support you... the old, their house, their rules apply.