I have taught violin to many children, not to foster outstanding musicians but to help them develop fine ability through the violin. I always tell the parents:

I am not instructing children with the intention of turning them into musicians. I am only making efforts wishing that your children will become people with fine and active brains, beautiful hearts and good personalities. Whatever field your children may go into in the future, I am confident that fostering strong seedlings now will help them succeed in their chosen paths; so whether or not they become musicians, please strive to the utmost. Even if they don't become musicians, those who have developed so beautifully will be people who can demonstrate fine abilities in many areas.

Once a woman brought me a child and said, "I would like my child to learn the violin as a hobby and as part of cultural upbringing. I have no intention of making him a musician; it will be fine if you train him just so that he can play a little."

"It's beyond me to adjust myself so that he'll be able to play a little, so I'm afraid I cannot take your child," I joked, and told her about the importance of training the mind: as long as she wants him to do it, she ought to guide him so that he will do his very best.

No matter what you have your child study there is no distinction between a specialist and an amateur. What is necessary is precisely to beautifully foster human abitliy. It simply depends upon how you think about it.