I have naturally very curly hair (think Shirley temple, only she's got nothing on me). I also work in a very professional position, so if I want my hair curly, it has to be in a shorter, bob cut. It's currently cut to my chin.
This struck me as yet another bit of evidence of the cultural bias that straight hair is more acceptable than curly, and (more sadly) that this has been accepted and internalised even by the Shirley Temples of the world. I hadn't realised that curly hair was inherently unprofessional, or that competence in a professional field would be judged on the amount of curls. As I say, that's rather sad.
I have very curly hair which is currently just below chin length. I also work in a conservative, professional industry, but thankfully, my hair has never been an issue. I always keep it clean and off my face.
That said, curly hair does often seem to be synonymous with messiness, and quirkiness. I've come across a few people who assume I have a "wacky personality" simply because my hair is curly. Whereas in truth, I believe my personality is actually somewhat shy and conservative!
To add to that, straight hair has been "in" in the last 15-20 years, which means that curly hair - during that time - has been deemed conventionally unattractive. It's tough growing up in a time when you're automatically deemed "not attractive" purely based on a genetic trait, so I really feel for the OP's daughter.
The good news is, is that according to my hair dresser, curly hair goes in 30 year popularity cycles. It was popular in the 1950s, 1980s, and is slowly becoming popular in the 2010s. As of now, the "slightly messy curls" look is becoming very fashionable. So not only is the coach silly, but she's also out of touch.