Cannot delete contact from Address Book
I had the same problem and I noticed multiple birthdays that I didn't recognize or didn't really need to know. 

When you're looking at the card, it should show where the information came from, in my case, the contact information came from LinkedIn. If that's the case, chances are there are more contacts you don't REALLY know, or if you do, you already have their birthday saved elsewhere. 

I went into system preferences, Internet accounts, scrolled down to LinkedIn and click. It shows all my preferences for LinkedIn and I just unchecked Contacts. Closed and opened Calendar and Contacts and all those birthdays and Contacts were gone..

Hopefully that helps!