"It is already morning, we are going to school."
Translation:Уже утро, мы идём в школу.
"собираться" means to plan/ to be going to do something. It is not about motion at all. And it requires a verb or an event to plan to go to.
Since "собираться" can also mean to pack up, "Мы собираемся в школу" means a completely different thing from what is suggested, i.e. either packing up your stuff before school, or making plans and arrangements to go there. Which are probably very similar.