My Dad was not thrilled when I first started cubing, I think he thought it was something that would take away from my school work. He turned into a big supporter of mine when I was able to show him that it did not affect my grades, and that I was getting better at it.
If your parents think that cubing is more distraction than helpful, make sure to tell them that it is the kind of hobby where in high school you can organize competitions at your school, either unofficially or officially if you can get a delegate involved. It looks great on a college application, and I have a line about cubing on my resume, and at a recent interview I did for a new position I was flat out told by the hiring manager that they kept my resume in the keep pile in part because of the line about cubing. Potential employers love cubing, because for them it shows that you know how to problem solve through a difficult problem, and that you are dedicated enough to learn a new task, even a difficult one.
Tl;dr You have to meet your parents halfway. They are concerned that cubing may affect your grades going into high school. Show them that you will manage your time well and still get your school work done, and also tell them that college applications and especially future employers are very often impressed by using cubing as a way to differentiate yourself. That's the kind of stuff parents like to hear, and it also very much happens to be true as well.