Many kids (male and female) who live in the country on farms and ranches are shooting .22 rifles before they're 10 years old; and they're quite good shots too. Their parents began teaching them gun safety and how to shoot well before they were 10 years old. They use their .22 rifles to shoot coyotes that are threatening the livestock. They don't use them for target shooting or shooting at cans.
I see nothing wrong with a 13-year-old learning to shoot. But, I see two problems you face right now; and it all depends on your parents and what they are willing to do..
(1) If your parents never let you out of the house, then how are you going to get to a gun range to practice shooting? Parents have to accompany a young person to a gun range, or else the young person won't be allowed to shoot. At your age, you can't just "show up" at a gun range by yourself.
(2) If your parents don't want you to learn to shoot and aren't willing to buy a gun that you can use, where are you going to get the money to buy a gun and the ammunition? You can't "rent" a gun and ammo at a gun range - you have to use your own gun and ammo.
The gun is YOUR responsibility. After you finish shooting, you have to make absolutely sure it's unloaded. Then, you have to take it apart, clean it, oil it, and put it back together and put it away (unloaded) in a safe location. That's something else you'll have to learn, before you'll be "trusted" with a gun.