I am not an expert but here is what I think is happening.
I create a new calendar event.
I then add attendees that I want to invite.
The attendees e-mail address is what they have set up as their iCloud ID.
The attendees do NOT use iCloud as their calendar (FYI I have NO way to know this ahead of time).
Because the attendees are registered in iCloud instead of receiving an e-mail notification of the event the notification is just added to their iCloud calendar (which they NEVER check).
End result is that the people I have invited to the event NEVER see the invite.
I would like to be able to force the calendar app to send e-mail notifications and NOT use iCloud. However, I am using iCloud personally to sync my calendar between my iPhone and MacBook.
I think that if all the people I invite would go into their iCloud calendar and select the option to receive event invitations as e-mail and not as in-app notifications all would be good. It is just NOT realistic for me to require all the people I invite to events to make this change.