How change default/primary calendar of a SHARED/co-owner calendar

I've seen plenty of posts about going to the calendar page, clicking the cog, selecting Options and then scrolling down to the Primary Calendar section to set your primary calendar. However, the only options in there are calendars I created. I created a family calendar and it is my primary calendar. I shared that calendar with my family and each of them are co-owners. However, when they go to the Options and look in the Primary Calendar drop down, that family calendar does NOT show. As a test my wife created a test calendar and then shared with me making me a co-owner. I accepted the share invite and then went to the options page and yet that newly shared calendar doesn't show in my list. Some of these calendars have been in place and shared as co-owners for a couple years and yet they do not show in the Primary Calendar drop down for any person in my family that did not actually create that calendar. This makes for trouble when on a mobile device, for example, and you are quickly adding a family calendar event because you always need to make sure you go back and manually change the calendar to the family one.

Thanks.