People at work go out in different groups & not everyone is invited. It's still arranged at work as that is the one piece of common ground. It's the same with school surely?
Many many years ago I was working at a hospital in city A, I was working my notice to move to both a new hospital and a new city, city B.
One person in the department in city A was getting married just after I left. But he made sure before he left that he handed out wedding invitations to everyone in the department except me.
It was meant to hurt.
The funny thing about it was that I would not have been able to go had I been invited, too far and no transport after I moved but that everyone else assumed that everyone had been invited.
I kept being asked about the invite because people were making arrangements to car share etc. A few people said, "oh he must not have got to you yet".
Nope, he invited 20+ people but not me. He ended up looking like a twat.
I was late 20s and thought the whole thing was childishly funny.
If I had been 5 I think I would have been incredibly upset.
Like it or not party invitations can be a tool used to bully and discriminate and that is what the school are trying to stop. They don't care who is invited to a party, they care about bullying.