I quit learning piano when I was small (after G2 exam). I told my mom that I didn't want to learn piano without giving her any reason. The true reason was because I was scared. I didn't like all those exams and Music Festival. It was out of my imagination that learning music meant exams and competitions.
Of course, I now understand that it's good to have a goal to excel. But how can I understand this when I was small. Practising is a burden. Music becomes torture.
Sometimes when I think back, I do regret requesting to quit. I really hope that my mom can understand my worries so that I don't need to give up. Actually, after taking the exam, I gained the confidence of continuing but it was too late by that time. We were much less vocal when we were small.
So try to understand your kid why he/she doesn't want to learn piano. You may find some ways to encourage and motivate them. Understand their concerns and worries. Let music be kid's friend.