Hi,
I wasn't able to remove Facebook event nor its birthday calendar. But I managed to add a working Facebook subscription webcal.
I like the calendars but the built-in integration wasn't working since no newly added events showed up. Also I wasn't able to add a new Facebook subscription webcal (that´s the solution if you like to have the Facebook calendar, you get the link from Facebooks web-version of the Event site) since IOS noted it was a duplicate. This is how I did it.
1. end all Facebook sessions (Facebook -> settings -> Security and login -> show more -> End all sessions)
2. change your Facebook password
3. get a new webcal subscripsion link to Facebook event calendar (Facebook web-version -> Events -> (to the right) Upcoming events)
4. add the link to a new calendar on your phone (Settings -> Accounts and passwords -> Add new -> Other -> Add subscription cal)
4. un-check (ie don't show) the default Facebook calendar in the calendar app
5. check (ie show) the newly added Facebook calendar in the calendar app