Q. Why was 13 chosen as the age for Bar-Mitzvah?
A. The first thing to point out is that Bar-Mitzvah was not fundamentally meant as a ceremony but a status. It denoted the age of responsibility for one’s own deeds, though this was marked by a simple ceremony from an early period in Jewish history (Sof’rim 18:5).
The concept is that physical maturity went with intellectual and moral awareness, evidenced, according to the sages (Avot d’Rabbi Natan, chapter 16; Zohar I:165b) by the ability to master the yetzer ha-ra (the evil inclination) and to live by the yetzer ha-tov (the good inclination).
Rabbinic commentary points out that Abraham was 13 when he committed himself to God and abandoned idolatry (Pirkei d’Rabbi Eliezer, chapter 26). At 13, Jacob showed his attachment to Torah and Esau his preference for idolatry (Gen. R. 63:10).
13 as the age for responsibility for the mitzvot is regarded as halachah l’Moshe MiSinai, a principle dating back to Sinai (rabbinic commentaries on Pirkei Avot 5:21).
Though 13 is the age of religious majority, there is an idea in more recent rabbinic writings that it has two levels – “basic” and “secondary” majority. Basic majority comes automatically when one reaches 13. Secondary majority is created by personal dedication to Torah study and observance.
Without the secondary level one remains Bar-Mitzvah in a merely nominal fashion (R. Nachum of Chernobyl, M’or Einayim l’Torah).
One must of course add that it makes a travesty of Bar-Mitzvah if the party overtakes the serious religious dimension of the occasion, especially if the celebration is non-kosher and morally questionable.