Correct, only one of you should have to create the iCloud calendar and then share with the other person via the share option.
I too had the same error message on a calendar that I shared with my Wife (we share about 6 calendars in total) and I found the issue to be that I had what's considered to be a special character in the description of the calendar. I used 'St. Michaels School' and I received the same 403 error. I have now changed to 'St Michaels School' with no error message and the share is working correctly on the devices for me and my Wife.