Preface: I'm old. I like to ruminate on topics. The conversation below is relevant to more than just flying. Use what makes sense, ignore the rest. TL;DR - There are no 'right' answers and no guarantees. Life is about the choices we make and only we can make them. The results of our choices may not manifest for decades.
Safety: Do some research and see if you can find a way to relate GA vs other fatality rates for things everyone does. Here are some starter stats. Since the activities are fundamentally different, you're not going to find a one to one comparison.
http://www.iihs.org/iihs/topics/t/general-statistics/fatalityfacts/state-by-state-overview
https://www.aopa.org/about/general-...l-aviation-safety-record-current-and-historic
https://safety.fhwa.dot.gov/motorcycles/
http://www.afn.org/~savanna/risk.htm
The problem with air crashes is that local crashes can make the national news. They are spectacular and get people's attention. Humans suck at risk assessment so something that's relatively safe (flying) seems more dangerous than something we do every day (driving) when it's not.
You as a safe pilot: I don't know you. If you are 20 and have had 5 car accidents, been in jail for public drinking, and smoke weed...as a parent I'd be suspicious that you had what it takes to be a pilot. If you've got your head screwed on right and can stick to a complex project until it's done, then I (personally) can't see any objection. Only you and your parents can figure that one out.
Your relationship with your folks - money: As long as you are financially connected to your parents, then they are in a position to affect your life. If you stand to inherit a scadzillion dollars and you care, then you may not want to **** them off. If you're like most of us and won't get or you just don't care about a huge inheritance, then once you control the money, it's your money and you can do what you want. Today high debt levels early in life make the situation different from when I was your age. I entered the adult world with a BS in chemistry, no debt, and none incurred by my folks. Again, i don't know your situation so what happens here is based on your life status and your choice.
Your relationship with your folks - emotional: If you have parents who raised you to be an independent human who takes responsibility for your actions, then you're likely to cause them concern if you fly but they'll get over it. If you have parents who are likely to consider you a child your whole life then you could be walking into a lifelong nightmare. It comes down to how you relate with your folks and how much the relationship means to you.
Money: Dear FSM flying is flying expensive. I'm doing sport pilot and it's $190/hr for plane and CFI. At a minimum I'll spend $7000 for the plane/CFI, $300-$400 for insurance, and a couple hundred more for books and software. Once I get through that, it's $120 for every hour I'm in the air. And that's just sport pilot. If you want to actually do anything where you might make money flying, then just keep ramping up the costs. I suspect there are ways to cut costs; the folks who work the desk at my flight center are all working on different certs so they may be getting a break on costs. Go talk to some, scratch that...talk to a LOT of people who are doing what you want to do and see how they're made it work. One bit of advice...NO credit cards; there leads a path to hell.
General musings: Nothing we do happens in isolation. If flying is something you really want to do, you'll find a way to make it happen. Will you wind up as an ATP and living the life? Who knows. My CFI got his ATP rating right when Eastern airlines went under and the market was flooded with experienced pilots needing work so his chance to fly for the bigs disappeared. My son never got his PPL but now he's back seat in a front line fighter. Life is weird like that. Be open to opportunities and work hard at what you do. You may never wind up where you intend or you may land somewhere better.
Side note: If flying is something that is in your blood, go talk to the military or the police (state, county, local, or game warden if they have aircraft). The recruiter will tell you sweet lies to get you to sign but it's worth a conversation. You'll need a degree to fly but there are ways to get your education paid for by Uncle Sam. This route is long, complicated, has no guarantees, AND you may wind up with a job where people are actively trying to kill you (and man will that drive your folks nuts!)
Good luck. May you lead an interesting life!