As already suggested: Take small steps. That's how I persuaded my parents.
I started out as making small experiments, like vinegar and bakingsoda in kinderegg shells (This was before my pyro hobby, IIRC I was 13 or so). Then I registered as member on a chem forum and read like a crazy. I heard about this "smoke bomb" with saltpetre and sugar. I wanted to buy saltpetre so badly, but my mom was against it. I told her I wouldn't make black powder, but only wanted to make fuses and a few smoke bombs. For a long time she wouldn't let me, but I kept telling her why it wasn't dangerous and such ( ).
She finally let me! Now my pyro could begin. I worked my way up slowly. Keep reading about the correct procedure of different kinds of deviced, this includes safety. Be sure to let them know how much safety you have. Twist the truth a little, it won't hurt. For example, at first my mom wouln't let me put black powder into tubes. Now I can make aerial shells and such. I can't make big aerial shells yet or salutes. But that is because she is worried about my neighbours. If I fired it at my holiday house, it's okay.
And I've also just bought an order on 1-6" shell hemis and 2-6" mortars. A 20 kg chemical order soon to come. I finally got my mom's permission.
I'm now 15 years old.