Probably too late, but Fakebook does not need your real birthdate. It wants it, to build a profile. Mine makes me 40 years old, so adverts are geared to things I would not be interested in.

But seriously, your exact birthdate is mandatory on some websites like banking and health. Why give the miscreant a sure-fire vector that with other stupidities like answering shared posts about your first pet's name etc, they can triangulate on banking or credit card details. They only have to win once in 1000 to make it pay, which might be over the phone. As long as it is not you!