I think everyone here has tried, albeit in a gentle and sensitive way, to help you understand the basic principles behind being paid for providing a service. Your responses are fairly typical of a young person, but no less annoying. So I'd suggest the following;
You were paid for a job. Your job wasn't good enough. Regardless as to whether your mate was out on the trail, or just bobbing along the road, the wheel went out of kilter just after you built it for him. If the same happened in a shop I'd be back like a shot. If you want to play at being a wheel builder, don't take money for it and fiddle around with your own wheels, not putting others at risk with your ego.
Why are you looking everywhere else for an explanation? Why not start with yourself; did you make any mistakes? Is there anything you've overlooked? The bottom line is that in receiving payment you become a service provider, so you are accountable for the quality of your work. I've been teaching long enough to know that kids like you simply don't have the ability to self-assess - you look for other variables as an excuse. Do you really believe that it couldn't possibly be your fault? Honestly?
And what's all this 'parents' crap? Are you kidding? Seriously? Are you going to wheel that one out whenever you screw up in the future - "...Er, yeah, the car crash couldn't possibly have been my fault because my parents wouldn't let me take the car out if they thought I'd prang it..." You sound like Vicky Pollard. Man up.
Give your mate his money back. Let him take his wheel to someone who's paid to do it and good at it. Learn from experience.
EDIT:
I realise this sounds harsh, but sugar-coating the facts will not help you. Good luck with whatever you decide to do. I'm off to shout at some year 10's...
(photo of my wheel after crash I spoke about earlier) 
