rageredsonic:

Your parents are probably right.  If you only have $10 per week to spend, there are probably better things you can spend it on.  You should understand that BitCoins are high risk, and I would not recommend that you buy them unless there's something you plan to buy with your BitCoins.

So, that said, if you still think you want them, here's what you need to tell them:

The point of an allowance is for you to learn how to manage money.  That doesn't mean spending it on things that your parents think you should.  It means giving it to you, and you learning to deal with the consequences of the choices you make.  If you lose a few weeks of allowance but you learn an important lesson about markets and economics, it'll be probably the best $50 you'll ever spend in your life.