I don't know about gossip fodder - isn't it totally natural to wonder? And while most do it privately you'll get some that openly (and possibly rudely) ask.
I would think it's human nature to subconsciously assign acquaintances into nice, neat categories - and when things change, it's disconcerting and we want to understand. Your situation is unusual with one fee paying child and one not. You've gone from being 'fellow prep school parent' which is our common ground, to something else. Some people just want to understand how to relate to you /your family. Or she might just be really rude and nosy.
I'm in Ireland, so the comparisons are likely to have cultural differences, but we do have some fee paying schools in my area.
I know kids who have moved from fee paying to state, and from state to fee paying and I am always curious about why. I'm curious because I want to know if I'm making the right decisions for my kids. If your kid moved, should I think about moving mine, etc. I appreciate parents who give me a reasonable explanation off the bat (but, I definitely don't pry and I'm not rude)
Other posters have given some good generic but friendly responses that will satisfy most curious minds.
My child wasn’t happy and we decided together to try a diff school.
I couldn't keep her in a school environment where she wasn't thriving.
It wasn't for her.
She's settling in really well to new school.
She likes the smaller/bigger classes, subject choices, etc etc'
She really wanted to take x subject and this school gas the best outcomes.
Her brother is really happy so he'll stay here.
Looking at the folks I know, reasons ranged from 'His father really wanted him to attend the same fee-paying school he attended, but it just didn't suit him.' to 'It's a rugby/soccer school and he's aiming to make it in rugby/soccer.' to 'He stayed with his friends for x number of years, but now study/future is getting serious.'