Not related to the Daf specifically, but:
From where do we learn that a boy is commanded in mitzvot from 13? A girl from 12?
On the Mishnah at the end of the fifth Perek of Avos, which lists the age of 13 as the age of Mitzvos, the Perush Rashi offers two sources:
1. From Shimon and Levi, who were called "Ish" when they killed the people of Shechem even though Levi was just 13 years old (if one calculates from his birth). This is also the source suggested by Bartenurah and Rabeinu Bachye there. If so, apparently the age of 12 for a girl is learned from the age of 13 for a boy, since a girl matures quicker (see Sanhedrin 69b, Bava Basra 16b in Rashi, Nidah 45a).
2. The age of 13 (and the growth of two pubic hairs) is learned from a Halachah l'Moshe mi'Sinai. This is also the source suggested by the Teshuvos ha'Rosh 16:1, who cites the Gemara in Sukah 5b that contends "[all] Shi'urim are Halachah l'Moshe mi'Sinai"; this is also a Shi'ur.
Below you will find our Insights to Nidah 45:2 and 48:2 which relate somewhat to your question.
Insights to Nidah 45
3) THE DIFFERENCE BETWEEN THE AGES OF MALE AND FEMALE MATURITY
OPINIONS: The Mishnah teaches that a girl reaches maturity at the age of twelve. The Gemara explains that this follows the view of Rebbi, who maintains that Hash-m gave more understanding (Binah) to women than men.
In what way does this make women mature earlier than men?
(a) The TOSFOS HA'ROSH explains that this means that Hash-m gives Binah to women earlier than He gives Binah to men. Hence, women are considered to mature earlier because their mental capacity develops at a younger age.
(b) The RAMBAM (in Perush ha'Mishnayos) explains that women mature earlier physically, and not just mentally, and they age faster than men (they have a shorter lifespan), and thus they also reach maturity sooner.
(c) The ROSH (Teshuvos #16) explains that all of the Halachic indications of maturity are Halachos l'Moshe mi'Sinai, and thus there is no obvious, rational reason to explain why women reach maturity earlier than men.
Insights to Nidah 48
3) THE HALACHIC SIGNS OF MATURITY
OPINIONS: The Mishnah and Gemara discuss at length the signs of physical maturity. We are taught that two pubic hairs are considered to be a Siman (sign) of maturity for Halachic purposes. Before the growth of such hairs, a person has the status of a minor, for we assume that his intellectual capacity has not yet matured.
The growth of hair does not seem to be physiologically correlated with mental maturity. Are the presence of two hairs just a physical indication that the child is physically mature, and therefore presumably also mentally mature (and such a presumption suffices, according to the Torah, to give him a Halachic status of an adult)? Perhaps, though, the Torah dictates that no matter how intellectually mature a child may be, he is not considered a "Bar Da'as" according to Halachah until he has two pubic hairs, for the presence of two hairs in some way bestows upon him the status of adulthood. Are the hairs merely a sign ("Siman") that the child has reached Halachic maturity, or are they in some way a cause ("Sibah") of Halachic maturity?
(a) The MAHARIT (Teshuvos 1:51) writes that the growth of hairs does not bring about Halachic maturity. They are merely signs that the child has matured. The Maharit points out that this is consistent with the meaning of the word "Siman," which the Chachamim use to describe the hairs.
This is also the view of RABEINU CHANANEL (quoted by the ROSH in Gitin 9:11), who writes that we lack the proficiency to determine Halachic maturity based on the mental sharpness of a child. Therefore, we have to rely on the Simanim to determine when he has matured. His words imply that if we could determine the sharpness of a child without having to rely on Simanim, the child would be considered mature even before the Simanim appear.
(b) However, the SHITAH MEKUBETZES in Bava Basra (56b, DH v'Li Ani) writes that Simanim actually bring about the Halachic maturity of a child, and they are not merely indicators of maturity.