Consider what
Rick Lax did. He went the "traditional" route and did everything that your type of parents (well intentioned & pragmatic) would hope for. Then, right before committing to a career in law, he did a brief foray into his long term passion for magic and he made it work because he simply
wanted it badly enough. There are
countless lessons to learn from his story and virtually anyone who is making a living in the industry. You only have one life; if you really want to be a professional magician, grab it. Make it work, and be prepared to play the long-term game with ups and downs. It will require learning about business, marketing, personal branding, social media, and many other skills. Luckily, at 15 in 2015, you have access to free and endless resources and examples on all of those subjects. (As a bonus, learning any of those skills would actually help you in any other career as well, so if your passion goes into another direction, you can take that value with you.)
...or you could do what I did and be happy as a hobbyist magician with a totally separate career.
Either way, I wish you the best of luck on finding something that brings you fulfillment. Also, you have my empathy for not having support from your parents. I'm sure they mean well, and hopefully they will leave some room for you to invest time towards your craft. Sometimes, the doubt the people have about your dreams can be used as fuel to prove them wrong.