Thirteen years is the age at which the Jewish male becomes bar mitzvah (“son of [the] commandment”). At this point in his life, his mind attains the state of daat—the maturity of awareness and understanding that makes a person responsible for his actions. From this point on he is a “man,” bound by the divine commandments of the Torah, individually responsible to G-d to fulfill his mission in life.
The age of daat is derived from Genesis 34:25, in the Torah’s account of the destruction of the city of Shechem by Shimon and Levi in retaliation for the rape of Dinah. The verse reads: “On the third day… the two sons of Jacob—Shimon and Levi—brothers of Dinah, took, each man his sword, and confidently attacked the city.…” The term “man” (ish) is used to refer to both brothers, the younger of whom, Levi, was exactly thirteen years old at the time.Thus we derive that the Torah considers a male of thirteen years to be a “man.”
But the context in which this law is derived is surprising. Shimon and Levi’s act seems hardly an exemplar of daat; indeed, Jacob denounced their deed  as irrational, immature, irresponsible and of questionable legitimacy under Torah law. Yet this is the event that the Torah chooses to teach us the age of reason, maturity, responsibility and commitment to the fulfillment of the mitzvot!
As Shimon and Levi replied to Jacob, the situation that prompted their action did not allow them the luxury of rational consideration of its consequences. The integrity of Israel was at stake, and the brothers of Dinah could give no thought to their own person—not to the jeopardy of their physical lives, nor to the jeopardy of their spiritual selves by the violence and impropriety of their deed. In the end, their instinctive reaction, coming from the deepest place in their souls—deeper than reason, deeper than all self-consideration—was validated; G-d condoned their deed and came to their assistance.
This is the message that the Torah wishes to convey when establishing the age of reason and the obligation of mitzvot. Rare is the person who is called upon to act as did Shimon and Levi. This is not the norm; indeed, the norm forbids it. But the essence of their deed should permeate our rational lives. Our every mitzvah should be saturated with the self-sacrifice and depth of commitment that motivated the brothers of Dinah.
Based on an address by the Rebbe, Shabbat Parshat Vayishlach 5725 (November 21, 1964)
 To the day; see Reshimot #21 and the sources cited there.
 The sages calculated that the equivalent age in a female, who matures earlier than a male, is twelve years.
 “And Jacob said to Shimon and to Levi: “You have besmirched me, making me odious among the inhabitants of the land…. I, being but few in number, they shall mass against me and smite me, and I shall be destroyed, I and my household” (Genesis 34:30); “Shimon and Levi are brethren: instruments of violence are their wares. Let my soul not come into their council, let my honor not unite with their assembly; for in their wrath they slew a man, and willfully they have maimed an ox. Cursed be their wrath, for it is fierce, and their fury for it is cruel….” (ibid., 49:5-7).
 See Likkutei Sichot, vol. V, pp. 150-152, and the sources cited there, for a discussion of the halachic pros and cons of the destruction of Shechem.
 Genesis 34:31.
 Cf. Midrash Rabbah, Bereishit 99:7; Tanchuma, Vayechi 10.
 Likkutei Sichot, vol. V, pp. 150-162; ibid., p. 421.