My oldest dd is in Year 5 so we are starting to think about/look at secondary schools. It seems to be these days that the child has a big say in which school he/she goes to.
I went to secondary school in 1983 and I'm sure in those days your parents chose your school! I don't even remember going to many open days.
10 is very young to make, or even help make, such an important decision. And even if a child likes or dislikes a particular school, parents often know better and have the maturity to look ahead into the future. I imagine many children will be impressed with facilities/extra curricular activities etc and whilst these are important, a child really wouldn't be interested in exam results or, ultimately, the quality of teaching.
Parents know their children best of all so they are best qualified to know which school would suit their child. After all, parents choose a primary school without any input from the child so why wouldn't the same apply?