Starlady,
I like your parents’ method. I have been pretty tough on occasion with insisting that kids get basic competency in an area (like swimming) and with insisting that kids try things, but I wouldn’t insist that they keep going if it wasn’t a basic life skill and was something they had no affinity/talent for.
With music for our oldest, we had an initial break-in period and some tweaking had to happen. Big Girl started with acoustic guitar and had trouble with finger pain, but her teacher (brilliant guy!) was able to give her some tips that allowed her to keep practicing without hurting herself. Also, we were initially having trouble with her saying she didn’t know what to do for practice at home. We were able to get over that initially by me booking her more lessons per week (this was the summer, so we had the flexibility and funds to do it), until she achieved some momentum (at that point, she liked her lessons, but hated practicing). Then she wanted to switch to ukulele and even bought a ukulele with her own money, and started playing it constantly and barely touched the guitar. We wound up switching over to ukulele lessons. I would never in a million years have expected to be paying for ukulele lessons, but here we are. She’s been doing music lessons for 3.5 years now, and I’m open to paying for more lessons right on through college if she wants to.
We still have little blips. We’ve had the usual fights over practicing, but have settled down to a routine of us expecting 4 15-minute practices a week. She often does more, but that’s our baseline, and I actually often tell her that a half-practice would be fine and that the important thing is practicing at least 4 days a week, but when she starts practicing, she almost always does a full practice. Her current teacher recently had heart trouble and she didn’t click with the new teacher and was talking about quitting entirely, but fortunately her teacher came back. Music is a huge part of her life now–she does a class at school, runs a club at school, has started performing in a community group and occasionally gives lessons to her brother and sister. Basically, it’s a whole new world. And the funny thing is that her dad is tone deaf and I avoided music energetically when I was in school (although we each have a musical sibling).
I’ve also given her a lot of latitude with regard to what kind of music she plays. Initially, she was just working out of the Hal Leonard textbooks, but as she’s gone on, she has more and more preferences with regard to what kind of music she plays. I sometimes give her a little nudge by buying particular books, but she has very strong preferences. Some books she might work with for a whole year, sweating over every single piece, while others she doesn’t have the time of day for.
I hope she’ll continue with her music, but even if she quits tomorrow, she’s already gotten a lot out of it, and she’s done so much work that if she ever wanted to pick it up again, she’d be able to.
tldr–It can be an uphill battle starting a new activity, but when the child has a genuine affinity for it, their interest and talent will eventually kick in.