Hear me out please.

why do you need to convince them? you should be making every move toward your goal that you can. if your parents dont like it and sell your kit on you... be prepared. hide a practice pad and drum sticks somewhere and us them as often as possible. when it comes time that you can move out; do so if necessary. if playing means that much to you than do not accept no as an answer. at some point your parents will respect you for going it alone and being man(or woman) enough to keep yourself afloat.

p.s. not getting anyone knocked up would be a solid way to not deviate from your path. also, read the war of art by steven pressfield.

Do the doctor thing. Drumming can't compete with that. Drumming for fun is much better than drumming to eat. Too much of a good thing (drumming) is not a good thing. You will be much more satisfied by doing both. I became an electrician, I work hard, but it pays great. Music is a nice 2nd income. And my musical journey is so enjoyable. It creates that balance we should all strive for. You don't want to be 45 working 70 hours a week between rehearsals and gigs making 500.00 a week saying Geez I wish I would have taken that opprotunity when it was there. There's plenty of room for both.