Okay but hear me out,

When Julian was little, his parents signed him up for classical violin lessons (because there is no way that two people who illegally augment their child and pressure him into studying medicine would draw the line at forcing musical skill) and he hated it. He hated the dreary songs he had to learn, he hated learning about composers from ancient history, and he hated the old battleaxes who served as his teachers.

But he never outright quits. He knows that quitting would disappoint his parents who would just add it to the list of things he’s ungrateful for. He can’t quit.

So he starts playing the fiddle instead.

Not only does he excel at it, he fucking loves it. He can play The Devil Went Down to Georgia with his eyes shut. He and Miles form an amateur folk music group (meaning no one hears them besides Keiko, Molly and Kira when she was living with the O’Briens). One time he got dragged out of Quarks, at 3 in the morning, fiddle case in hand, having insisted on playing The Dixie Chicks Experience for the in-house entertainment.

TL;DR Julian Bashir gets back at his parents in the most Petty™ way possible.