Here is a message I received from BranShea:


You are no pedant in this anniversary matter but simply right: We all have only one birthday i.e. the day we were born.

Only the English and the German language give: Birthday and Geburtstag (mentioning birth).

Dutch-verjaardag
French-anniversaire
Spanish-Cumpleaņos
Italian-anniversario

These four languages at least just give : the adding or passing of another year. Like what anniversary means.

So it is more correct to use anniversary than birthday.