I dunno about the documentation myself, I forget how/when I learned that.
BUT...you don't enter your email address to share your Calendar, you enter the email address of the person you wish to grant the share TO.
So if you are Bob and want to share your Calendar with Fred, you right-click, share Calendar, enter "Fred@xxx.com"
Fred will receive a message in his Zimbra webclient which says "Share Created" and has a link in it to accept the share. Once the share is accepted, the Bob calendar will show up on Fred's Calendar view page.
On our system, those "share" messages only seem to show up in the Web client and not when you use an external client like Thunderbird. (I mention this as an aside because I don't know if it's "supposed to be" like that or not. Maybe it'll be different in your environment.)
There is a way to open the Calendar using the "path" if you've been granted permission, but I forget the details. You right-click on your Calendar again and select "open other Calendar" I think, and I think you use a format something like "/mailboxname/Calendar"