This is a pet peeve of mine also. I’d venture a guess, that in cases like these, the biggest reaction (as has already been suggested) they’re trying to provoke is an emotional one of protection. That said, you also see this anytime it’s being used in a derogatory sense (IE: Miley Cyrus is still a ‘little girl’ dressing like a slut!) and it’s all about infantalizing them. Considering we’re a society that likes our labels, I’ll never understand why ‘teenager’ isn’t a good enough term for a person aged between 13 and 19. It has always infuriated me (hyperbole alert!) when others (excluding their parents, an issue best taken up with them) refer to them as children, or boys and girls, especially when they are over 18 and the media / law correctly calls them adults.
So, no, you’re not alone. And I say this as a 44 year old step-mom to a 24 year old man. Go figure.
This reminds me of that admittedly outdated adage that says your son is your son till he takes him a wife, but a daughter’s your daughter to the end of your life. I think this only goes to show that there’s still some patriarchal cultural baggage with regard to female adolescents; but on the other hand it’s arguable that a fifteen-year-old girl is likely to be more vulnerable than a fifteen-year-old boy, in a very real sense. Fathers of daughters that age do worry a lot more, I’m sure.
I readily admit that this is my own baggage, but I find this highly offensive. I understand it, and understand how as a father you’d feel that way, but if I were your daughter and you ever told me anything like that, I’d be quite annoyed. I’ve always prided myself on being independent, competent, and not desirous of any sort of special treatment or consideration simply because I was born female. Why can’t we teach our sons to be men and our daughters to be women, not try to keep them as “little girls”?
Sigh…I know, it’s rhetorical. And I’m not knocking you for how you feel. But I’m very glad you’re not my dad. I think we’d clash a lot. 
Well, depending on how stringent the terms of the bet were, you’d lose. The sheriff is female.