Hey, I'm in the same boat. My parents are scared crapless that I'll hurt myself and break a leg (literally). I told them snowboarding isn't that dangerous. If your parents believe in facts here are a few that work tremendously in your favor:
1: You have a higher chance getting a concussion in soccer than snowboarding, and you're not wearing a helmet playing soccer.
2: If you fall on a snowboard, the board helps slow you down, which usually is safer. Compared to skis, if you fall, you can twist your knee, keep sliding down the mountain, etc. You can leave out the usually part
3: You have a higher chance dying in a car crash today than getting hurt/getting a concussion while snowboarding.
Oh by the way I'm not sure if those facts are true but pretend they are. Hehe.
You can tell them that you'll stay out of the park or be a bit more careful. Continue as usual. If you get hurt again tell them you tripped in the lift line and the lift was a fixed grip so it didn't slow down and smashed into you, knocking you down a slope headfirst and getting you run over by the lifty reaching for the stop button.
But remember not to push yourself too far. I've tried not eating or drinking for a good hour while being tired just to get in a bunch of runs before the resort closes. That's just stupid. There's always next time. If you get hurt, next time will be in weeks, possibly months, possibly never. Don't do it. I fell and sprained my wrist so bad I could barely lift my board. Didn't tell my parents, though, but if I broke my bone, some serious shit would have gone down
OR you could get one of your parents to start skiing or snowboarding. Hopefully they'll see how fun it is and how much it means to you (and everybody else). Snowboarding doesn't get you hurt directly. Your choices get you hurt.
Sorry this is a lot of stuff from a fellow teen snowoboarder