I seriously stunk at the cello... but I paid for my own lessons and instrument for three years, and enjoyed every minute of it. About halfway through the second year, my teacher, very gingerly, asked me how I felt my progress was coming along, and was I meeting my own goals? I assured her that I stunk at it, but was enjoying it tremendously, so if she didn't mind being paid to tolerate really bad playing, I'd like to keep working at it. She was relieved, and we kept going until I left for college 350 miles away. (Turns out, I have a really small "wingspan", and not a lot of grip in my hands, so stringed instruments will always be challenging.)
It was actually a delight to have to WORK for things! I took ballet, too, even though I was a vastly imperfect body type for the discipline, and had no illusions about being a star, a professional, or even a small-town ballet teacher some day. I just wanted to dance. I never participated in a single recital (the studio didn't do them, though we could participate in stage performances of classical pieces on occasion).
The mom is absolutely off-base. Her children may have a gift for graceful dancing, but that doesn't mean other children shouldn't give it a whirl. Working hard and enjoying yourself are both worthy goals, alone.