iCloud calendars not allowing editing when sharing

My office is trying to switch to iCal for our scheduling. Each person has their own iCloud account and own Mac computer. Those of us who have iPhones have only been able to successfully share/sync our calendars from our iPhones themselves. Those who do not have an iPhone but have an iCloud account are having issues sharing their calendar so that everyone else can read and edit. Their calendars are public and their settings are set so that we can read and edit. So when sharing, we can view their calendar, but can't add to it (it wont show up in our list of calendars to change to). Any idea what's going on??