Well, I for one understand where your folks are coming from. Wrestling's a gruelling sport. Rick Steiner doesn't want his kids to get involved in the biz because of how tough it is and Billy Gunn doesn't want them to either. He didn't give a reason, but I imagine he was thinking along the same lines as Steiner. The risks to your body are real and the lifespan of a wrestler isn't long, compared to other walks of life.
I would say if you really want to go into wrestling, it's your decision, but take heed of the fact that the travelling schedule will be tough and you'll see many venues that you didn't before and this might be very disorienting. I myself wouldn't become a wrestler because I'd never know where I am or who I'm talking to. Some wrestlers are genuine people who play a role, but others, as some have commented, stay in character, in and out of the ring. Also, territory can be tricky and making enemies in other states can become an ordeal.