Unable to share iCloud calendar

I have been trying to share my iCloud calendar with my co-workers for several days. I follow the correct sharing procedure, yet those I invite never receive invitations. They have been able to share their calendars with me, and I can see their events and sharing info just fine. I have tried from the web-based iCloud calendar, the desktop app, and the iPhone app. I can share publicly from the web-based calendar, but I need to be able to share Privately, so invitees may view and edit.