YABU!
If my parents had had the money to send any of us (3 kids) to private school, it would've been my brother.
He's very academic - only has to read through his work once and absolutely aces his exams, excels at Maths and Science but is very withdrawn, not great with social situations and needs to be given a good push to make him realise that he won't get by forever just reading the work once and heading into the exam (although he probably will, the lucky sod) . Private school would be ideal for him.
My sister isn't academically gifted in the slightest, struggles with her work, she puts a hell of a lot of work in but sometimes still doesn't quite get there, and yet she's a menace on the football field, an absolute star at PE and could conceivably be looking at getting a sports scholarship to uni in the next few years, but private school wouldn't be for her, as she doesn't thrive under that kind of pressure. She is a social butterfly, very chatty (sometimes disruptive but my parents are working on it), and is thriving at state school.
Meanwhile with me, the only private school my parents probably would've even entertained the idea of sending me to would've been theatre school. I've always been a bit more of a dreamer, creative, musical and very much into theatre, but I was also very 'head-in-the-clouds' and I need the sort of pressure a good state school gave me - firm, without being a complete hotbed of pressure, because there's only so much I could take before I'd start to rebel against it. I got very good GCSEs and A Levels (for a state school pupil, compared to average), but only because I worked bloody hard for it.
Just shows how three kids from the same family can be so different and can do well in different environments - if the family has put that kind of thought into their childrens' personalities and where they'd fit best, they're absolutely not abusive in that respect.