The advice here is better than that. Sorry but the Gurus, one of whom will hopefully be here soon actually sit on appeals panels.
No you can't argue DC should go to X because she is bright (unless it is a Grammar school appeal). But you can argue that she should go because she is disadvantaged by not going as she has a demonstrated interest in "hairdressing" or whatever.
FAP isn't so important at this age. What you want to show is that the school can and has taken more than their PAN (that they can physically fit another child in).
My DCs schools all regularly go over their PAN.
You won't to work on showing (with the others who appeal) how little prejudice to already accepted pupils taking extra ones will cause.
And how harmful it is for your DC not to be accepted and why. What unique things this school can offer which match your DCs talents and interests (or even SEN).