I am having a strange problem!
I have had trouble with my company's Exchange mail (Outlook 365).
So, I tried deleting and re adding the account.
For a month, it worked just fine, but now I tried to delete and re-add but couldn't do it.
The strange part is that even though the account is deleted, I have two calendars from my company still present!

Does this has something to do with the inability to add account?
How can I do it without having to flash the phone?

Got same issue. Cause : my old account of calendar was declared as default calendar in settings, applications, calendar. I think it's a bug.
I found 2 workarounds on this forum. Some delete the /home/user/.calendar/db file. Others edit this db file with a SQLite browser for deleting corrupted entries. I choose the second option and it worked for me. I used devel-su plus develsh for managing this very well hidden file.