The kid and Melinda met a boy ghost together, and after that the kid's mother got angry saying "Why would you encourage him?" Does "would" mean past willingness or present one? It's always confusing!!!
kid- She never believes me.
mel - Sure. We all had a nice conversation.
mother- Why would you encourage him? You think it's healthy for a boy his age to have a make-believe friend?
In this context it's simply a shorter way of saying 'Why did you think it would be a good idea to encourage him?'