If I remember correctly, when I first installed Facebook on my phone I was asked if I wanted to link my Facebook contacts. Adding the birthdays of your Facebook friends is one of the things which happened when linking the Facebook contacts.
Try going into settings > accounts > Facebook and make sure contacts are not synced.
You may also have to go into the Facebook app menu and make sure you are not syncing contacts there.
It could be that they were synced at one time but now they are not. Unfortunately, if they were once synced simply unsyncing them may not actually remove the data already in the calendar. You may have to manually delete the data.
Another thing you may try is to not display the Facebook contacts. Don't know if when you display the contacts, the data from those contacts(including birthdays) may populate the calendar.
My phone isn't giving me an option to remove them manually. The only options I get are "copy" or "share via". I don't have my Facebook contacts displayed either. Any other suggestions? Thanks
Try going into settings > applications > Facebook
From there clear both data AND cache.
Then to be on the safe side go into settings > accounts > Facebook and remove that account.
You will then have to sign back into Facebook when you start up the app. If it asks to import or sync your Facebook contacts, simply say no.
If all else fails, try a factory reset.