Read-only Calendar???

If someone has shared a calendar publicly and you have subscribed to it, it will be read-only. If someone has shared a calendar privately it's their decision whether the calendar is read-only or whether you are allowed to write to it.

If this isn't a shared calendar, but one of your own, then something has gone wrong and we would need a lot more information as to what exactly the situation is, including where you are seeing this and your Mac's operating system if it's there.

This page give info on the Birthdays calnedar:

http://support.apple.com/kb/PH2676

It says:

'You can’t modify birthdates within iCloud Calendar. To modify a birthdate, use iCloud Contacts; changes are reflected in iCloud Calendar within a day.'

So I would guess the first thing to do is to give it a day or so and see whether the calendar catches up with the contacts deletion.

Is this a shared calendar?

Are all these birthdays in a separate calendar from the others? - if so can you just delete the calendar, assuming that it doesn't have anything else you want to keep in it?