Resolution here
Hi ptb127 (& other iPhone annoyed users)....
I feel your pain guys
It was possible to address this issue for me as I have a Jailbroken iPhone... If not, this is not gonna be the solution for you - sorry....
Before proceeding any further make sure you do NOT have any Calendars named 'Birthdays' and if so... make sure you rename them, in order to leave just the inbuilt Apple calendar using that name.
So here you go:
1. Get Cydia on your phone (usually) available upon jailbreaking the device.
2. Install SQLite3 (thanks to Saurik) from Cydia - if you're unable to see SQLite3 in the search result change profile to Developer rather than Hacker or User.
3. Install OpenSSH too.
4. SSH to iPhone and hover on to the Calendar directory where Calendar.sqlitedb resides ... in my iPhone 3GS case, which is running on 5.1.1, it is located in /User/Library/Calendar
5. Run SQLite manager by typing:
sqlite3 Calendar.sqlitedb
6. At the SQL prompt type the following
A) to view Birthdays records type:
SELECT * FROM Calendar WHERE Title = 'Birthdays';
B) to delete these records type:
DELETE FROM Calendar WHERE Title ='Birthdays';
You can now check your Calendar App... which now should be not showing it. Hope this method helped you ridding off that annoying Birthdays calendar.
Good day