That's a tough one.
My son started off in traditional martial arts (around age 10). He was a walk-on for wrestling in 9th grade and made varsity in 10th grade. He's since taken up Brazilian jiu jitsu, grappling, and Muay Thai. He's been doing MMA for about 2 years.
You've obviously done some research, and the figures about football concussions are frightening. Still, of course, you can experience head trauma in boxing, too. And my son (who's continued wrestling and is now probably at the level of a pretty good college competitor) recently broke his arm when he missed a takedown. Really ugly X-ray. Had to have surgery. But he appears to be healing well.
So, what do you do? First, seriously, try appealing to your dad. I don't know about your family, but moms tend to be a lot more protective and fearful than dads. My wife is really very supportive of my son's MMA activities...but she's never been to any of his fights. Never been to any of his BJJ or grappling matches. And only went to one or two of his wrestling matches. It makes her too nervous. And, frankly, many moms are like that.
With her, I wouldn't get into the "defending myself" argument, partly for the reason you note. Instead, stress the physical benefits. Boxing and wrestling take a lot more cardio than football. There were a number of football players who also wrestled on my son's team. Football is a fall sport and wrestling is a winter one, so the football players would miss a week or two of wrestling, then show up in November or whatever. Even though they'd just played a full season of football, they were out of shape compared to the wrestlers. I can't imagine boxing being more draining than wrestling, but it could be close. And so your argument there is that it's better conditioning than you'd get with football.
Tell her that boxing isn't all about hitting the other person in the head. There's a lot of body work, too. A lot of movement. Lots of hand-eye coordination activities. But, strategically, consider making much of your pitch to your dad.
Hope that helps.
They won't let you box but they're happy with you wrestling? You're far more likely to get injured doing wrestling you know.
Amateur boxing is actually quite safe. There is no strong link between amateur boxing and brain damage - the potential is still there but you never hear of amateur boxers suffering from dementia pugilistica. It's a whole different game to pro boxing. You have to win by points - knocking your opponent out doesn't automatically make you the winner like it does in a pro match.
I like your idea of having a wrestling/boxing background. It's an excellent base to have for MMA, if you ever wanted to get into that. Maybe mention this to your parents? Learning boxing for MMA competition might sound a bit better than just 'self-defense'.
Once you start boxing, you won't go right into physical contact. You'll learn the ropes, working the mitts, speed bag, heavy bag, and getting into shape. That usually takes a month or two to master then you might get thrown into sparring. In sparring it ain't like professonals, its like amateurs. You got head gear and you got all the protection you need. Same with amateurs. If your serious about it, you will be wearing head gear in the amateurs which won't cause to much head problems.
I would tell your parents about the head gear. Tell them you won't be doing physical contact until you learn to defend yourself and even after that you will have headgear. You don't take the headgear off until your a professonal, which would be years away
i think wrestling is a disgusting game
I am 14 and I want to box, but my parents won't let me because they don't want me to get hit in the head. I would be able to understand this, but the reason I don't is because they are ok with and even encourage me to play football (American). Now most people know that in football you run a very high chance of concussion. Probably the same amount of risk, if not more, than boxing. I have good grades, mostly A's and B's. She says I can train in it, but that's not enough to me. I want to compete. The club that I want to go to doesn't let you fight until at least like 6-8 months of training, and I'm ok with that, as long as i get to compete. The 6-8 months of training would probably make it to where I wouldn't get beat to bad and it would be safe. I don't even want to do it as a main sport, because my main sport is wrestling. Can someone help?