Ahhhh. Okay. You don’t want to use the shortcode option for the field name then. The shortcode option in the field list is a display-only field, and it executes the shortcode that you put in it. It’s basically the same thing as the ‘Content Block’ field, except that it’s just for a shortcode. You stick a shortcode there, and it runs that shortcode in that spot for everyone, just like you had put it in a page.
You’ll probably want to use a plain text field for that. If you want it displayed on their profile (as the actual calendar and not just the text of the shortcode), you’ll probably need to write some code to do a custom display for that field, but some caveats:
Shortcodes are not meant to be user-editable, and it’s dangerous to allow them to put their own shortcodes in a user-editable field, because they could put in a shortcode that goes to something other than a calendar and expose private backend information depending on what plugins you have installed. It would be better to allow them to specify arguments for it, and have your custom display code always run that specific shortcode just with their arguments.