When a child becomes Bar or Bat Mitzvah we say that they are becoming adults, but in our modern world the age of 13 seems a little bit young for being considered an adult. All the other markers of adulthood in our society come later: driving license at 16, right to vote at 18, etc. So we might wonder why Judaism considers adulthood to start at a significantly younger age.
One answer to the question is that the rules of Judaism developed in an earlier time when many of the responsibilities of adulthood started at a younger age, but this still doesn’t answer the specific question of why the Bar and Bat Mitzvah happens at 13 years of age.
In our Torah the age of 13 does not appear to be particularly significant, except for the fact that Ishmael was circumcised at this age (thankfully we follow the practice of Isaac who was circumcised at 8 days old). So we have to look into other texts.
In the Mishnah, in a section called Pirkei Avot, the Ethics of our ancestors, Rabbi Judah ben Tema offers us a schedule for our children. He says that ‘5 years is the age for the study of Torah, 10 years is the age for the study of Mishnah, 13 years is the age for becoming subject to the commandments, 15 is the age for the study of Talmud, 18 is the age for coming to the chuppah (bridal canopy)’ and so it continues right through until the age of 100.
He does not say that a person becomes an adult at 13, instead he says that a person becomes subject to the commandments at 13, which by extension means that the person is treated as an adult. In another section of Jewish law (Talmud Niddah 45b) it says that the vows made by a person of 13 years or over are binding.
Becoming Bar or Bat Mitzvah means becoming a son or daughter of the commandments, and so it makes sense that it marks the age when a person becomes subject to Jewish law.
From an anthropological perspective seventy percent of primal cultures have some form of formal adolescent-initiation practice; significantly as with Bar and Bat Mitzvah these rites precede marriage, reproduction, and adult responsibilities. And from a neuroscientific perspective there are benefits in having these rites of passage before adolescent hormones and emotions begin (you can read more about this here http://www.huffingtonpost.com/william-grassie/neuroscience-of-the-bar-mitzvah_b_1126955.html).
In this way the Jewish choice of 13 as the age for becoming an adult clearly has benefits which can be seen in the wider world and adolescent development. Perhaps this is part of the reason why the institution of Bar and Bat Mitzvah has not only survived in our Jewish culture, but thrived to become a central rite of passage, and a central moment in most people’s and most families’ Jewish journeys.