Someone at Google doesn't seem to like Christmas, or more specifically, the entire month of December. In a rather glaring omission, the People app in the latest version of Android (v4.2) does not let you set any date in December as the birth date of a contact (see screenshots above).
Update: See Google vows to bring 'December' back to Android 4.2 "soon"
The issue was first reported to the Android development mailing list on November 14:
Today I was inserting birthday of a friend in my contact list so that I can sync the birthdays in my calendar. I noticed that the December month is missing. When I pressed new event the calendar came but it was not having the option for the month December. I'm using Galaxy nexus running on 4.2 jelly bean which I installed yesterday on 14 November 2012.Just to be clear, the problem is that the option is missing from the front-end. If you add a contact via Gmail, the information syncs up just fine with your phone. Just that you cannot add/ edit contact details to include a date in December.
Please help me with this as I use the calendar a lot