Once my parents figured out that I was going to do it anyway, they were actually quite supportive - they bought my first lid for me, presumably on the principle that if I was going to do it then I ought to be kitted out properly.
I think now they are pretty resigned to the fact that I am going to keep on riding whatever. My dad occasionally makes comments to my wife (who I introduced to biking) about how she should buy a nice car (rather than the combination of shitty car and bike that she has), but I think he's given up on me
Unfortunately, if your parents don't ride, then the only things they hear about bikes are people doing stupid things and getting hurt. I've done tens of thousands of miles on bikes with (touch wood) no harm coming to me. One of my best mates has probably racked up some sort of 6 figure mileage and fallen off once - on a trackday, and again with no injury. But unless you ride bikes you don't know about the majority of people that spectacularly fail to crash and die.
In terms of constructive advice...
- don't do stuff behind their backs, but be prepared to do it whether they approve or not - not in a "f*** you I won't do what you tell me" kinda way. Just have the means to pay for everything yourself, have a plan of how you are going to pass your test, all the safety kit you will need (buy this before the bike). Just try and give the impression that you know what you are doing and you have considered everything.
- consider taking it fairly slowly. Think about planning to buy a 125 and racking up some miles on that - you can point out that it's a nice small, safe bike, and you're not rushing out to buy some crazy big bike. Plus it's cheaper for you - I spent maybe a grand on my first bike, kit, and insurance combined. And frankly, I had great fun riding my 125.
- again, when you get round to your test, do everything by the book and make sure your parents know that you are taking it seriously. No "restricted" sports bikes.
Ultimately, if you can't bring your parents round by reasoned argument and showing you've considered it carefully, then you're fecked till you move out.
Dunno if any of this helps.






