Summary

When an administrator invites a guest to a site that does not have a default access group under the Guests tab, a generic error message will be displayed:

Unabel to add USER_EXAMPLE

We couldn't send your invitation. Try inviting that user again.

 Inviting the user will not work.

By using the browser's console when the issue happens, the following error can be found:

{"key":"noDefaultGroup","context":{"message":"No default group for Product: Product}}

{"key":"noDefaultGroup","context":{"message":"user account is disabled for Product: Product}}

{"key":"inactiveUser","context":{"message":"Not all users have active AtlassianId account"}}

Suggestion

This is a suggestion to improve the error message in order to clarify that the group must be added as a default one under the Guests tab so users instead of asking the administrator to try again.
Use browser dev toll to see the actual error message