Thank goodness for Sav'nBass and NYCbassist. I can't believe what a bunch of artless old fogey responses you've gotten. Pretty pitiful on a musician's site. What a lot of "just accept that you will not make a living doing something you care about." My, haven't a lot of you developed a horribly jaded view of existence.
EVERY choice you make for your life will contain compromises. If you choose to follow the path your parents are suggesting, you will compromise your desire to follow your own path. If you attempt to establish a career as a professional musician, you will compromise all sorts of income security possibilities. Every choice will have its compromises, and you have to determine which ones you can most comfortably live with. The great majority of the responses here assume that you will develop the same desires for your life as they did. There is no reason to believe that this is so.
My degree is in Theatre with a focus in Technical Theatre. I do all the design work for a small college. Just as in theatre and film, in music there are FAR more jobs in the technical areas than in the performance areas. If what you love is music, study music. You may enter the field thinking you're going to be a professional musician, but you may develop an interest in another part of the industry where there are more jobs and more security. Regardless, you will be working in the field you love.
There is tremendous truth to the adage: "find something you love to do, and you'll never work a day in your life." The recommendations here that you find a job in an area you have no interest are a recipe for a miserable life. It really is possible to study what you love AND have a practical approach to finding a career, and it's also perfectly acceptable to decide to devote your life to a career that is not considered practical by most others, as long as you are willing to accept the consequences of such a choice.
No matter what anyone else tells you, the choice is yours, and your life depends on it. I know it's hard making such life shaping decisions when you are so young. Do as much research as you can in your area of interest, and then try to make a decision based not just on your interests, but also on reason and reality.
Good luck.