I have heard at various times that celebrating a birthday is not a Jewish thing, a sevara I don’t pretend to understand, but people repeat things until even silly sevaras becomes “canonized” in popular folklore. It came to mind when I saw the discussion of Adar 7 in yesterday’s daf, Nazir 14. The gemara discusses whether making a kabbalah “like Moshe on 7 Adar” constitutes accepting nezirus or not. Tosfos explains the gemara's safeik: on the one hand, 7 Adar is the day Moshe died and many people took vows of nezirus in response to the tragedy; on the other hand, 7 Adar is the day Moshe was born, a day of simcha not in the spirit of nezirus. Which aspect of the day did the person have in mind when he/she made their kabbalah?
If Moshe Rabeinu could be happy on his birthday, and if klal yisrael could be happy on his birthday, what could be wrong with birthdays?
While on the topic, what is the idea of tzadikim being born/dying on the same day? R’ Tzadok haKohen explains in Kuntres Divrei Chalomos that a birthday marks the pinnacle of a person’s mazal’s influence. This power boost to the neshoma can help a person overcome all kinds of obstacles in life on that day. For a tzadik who is already on a high madreiga, this boost elevates the neshoma that it can no longer be held in a physical body in this world. The fact that a neshoma departs the world on a birthday proves that the departure of the neshoma is a result only of a great aliya.