Why is that if a child plays soccer 5 days a week, nobody ever says that his/her parents are pushing him/her too much?
They probably do. Although I don't think it was anything you said that triggered the comments.
Pushy isn't so much the problem anyway imo from the pov of developing a skill. I think most of the pushy stuff is where the push is towards celebrity and fame rather than necessarily pushing someone to be good at playing the piano, maths or acting, or whatever else.
e.g [although you aren't suggesting doing this] There's a certain "freak show" element to those young kids you see playing piano on TV. That's nothing to do with how much they are or aren't pushed into the playing aspect. Largely, from the audience perspective, their playing is secondary to the fact they are a particular age.
But since you brought it up, can I ask why a competition? I've no experience of competition personally, [nor of playing the piano at a young age for that matter], but from everything I've read here about competitions, what they are like, why folk do them and so on, I'd be more inclined to look at something where folk play music together, rather than against each other. As you appear to do with the community orchestra.