The Birthday Calendar is a "subscription", and subscriptions are not synced with the iPhone (for some reason)..
The only way around it is so export the calendar, then re-import it .. making it a normal calendar type (ie, not a subscription), then then that will sync to your iPhone...
Only thing is, it won't automatically update if you add/update/delete birthdays in the address book, so you have to re-export and re-import again etc..