I'm 26 and I had someone ask me this right after I graduated in May. It seems to be the inescapable question everyone is faced with at some point. The problem is, it's becoming increasingly difficult to answer. Having switched majors and careers more times than most people switch socks, I've had my fair share of answering this question. I also used to coach prospective freshmen on degree decisions in my last couple of years at BU.
Before I got my dream job as the Assistant Director of NCMS, my answer had been, "Whatever people will hire me for," which most people are less than pleased with. Here was my predicament: I have a degree in physics, was an engineer for 2 years, have a degree in music, and was working at a music school and have some decent playing credentials. So, should I have answered, "I want to be a musician and perform all day!" Well, no, that's not true. That lifestyle is too unpredictable for me. I need some stability, financially and with my schedule. Plus I don't really think I could gig full time as a clarinet player (it's possible but pianists and singers have it much easier). So, should I have answered, "I want to be an engineer, but do music as a hobby." Well, no. I've spent a significant amount of time and money studying music at a professional level. It's not fair for me to say it's just a hobby.
So how do I answer this question? "I want to be an engineer and a musician," is what I was trying out for a while. "What? Won't that be really difficult?" came the cries of the disbelievers. You probably have heard that we are becoming a freelance economy. Well what a better way to have security in your freelancing career than to diversify your income streams. Is 10 hours of gigging, 10 hours of teaching clarinet, and 20 hours of freelance programming really that music different than a 9-5 desk job?
My point is, don't be afraid to pursue everything that you love and take seriously, at a professional level. Especially with the modern job market, the only thing that's unreasonable is someone reacting negatively to someone else saying they want to do more than one thing. Want to be a comedian/actor/model? Go for it! Want to be an engineer/entrepreneur/musician? I tip my hat to you! Want to seriously pursue sousaphone and clarinet? I think that's great! Not for nothing, I actually got my first paid clarinet gig before I got my degree in music, but that's another post entirely.