Because ANY broadcast, public or private, is not permitted. If it was just limited to public re-broadcast, it would say so.
The same applies to any pay per view type event. They want people to buy the ticket to view it live, and don’t like it when someone re-broadcasts that content allowing others to avoid paying. Even in private.
Private homes are fine to hang out and have friends view. Using the internet to provide free access and avoid buying a virtual ticket, is not. Discord is not your living room.