Instead of just telling her no, try this approach…and how old is she anyway? 12 would be a little young for this but 14 or so on up it is right on.
Sit her down and treat this exactly like you would if she said she wanted to be a Doctor, a vet, an astrophysicist or whatever. In other words, treat it seriously and ask her to view it like a serious option.
What career around horses does she want? Does she understand she would have to be an employee of somebody else? Where? How is she specifically qualified for that position? What does it pay? Who would she work for? How would she qualify for it education wise? What does she need to do besides ride?
Usually, young to mid teens have this vague vision of their own training barn and riding the GPs but they have absolutely no idea how to get there and sort of assume it will simply happen if they want it bad enough.
Ask for specifics and you don’t look like the bad guy saying no all the time. Ask them to map out a plan for the next few years.
And do share every penny of the monthly cost of her horse to give her a perspective on what kind of income she will need to own her own horse. A W/S can’t provide enough labor in the kind of show barn that would actually help her gain a reputation to cover the 2k or so a month for all expenses.
You can also share barns like mine, an average high quality AA show barn that does take working students and can be a reputation builder, get anything from 30 to 50 inquiries a month for W/s positions. They offer only to those referrred by known pros and they cannot bring their own horse.
Just make it black and white and put the ball in her court. Don’t say absolutely not, given the hard facts she’ll probably do that herself.