The parsha of Toldos contains the source for the bracha made on the occasion of a Bar-Mitzvah. When Esav and Yaakov reached manhood (vayigdelu), Esav became a hunter, while Yaakov entered the tents of study. The midrash comments that from this verse we derive that a father must attend to his son until the son turns thirteen. At that time the father says, "Baruch shepetarani meonsho shel zeh" (Blessed is He who exempted me from the punishment of this [boy]).
The Magen Avraham (225:5) explains that after Bar-Mitzvah a father is no longer punished for the sins of his son. The Levush interprets that after Bar-Mitzvah the son is no longer punished for the sins of his father. Both understandings share the same difficulty: Why isn't the same brocha recited for a daughter and by a mother? The Pri Megadim (op.cit) raises this question and answers based on very questionable assumptions.
Perhaps the bracha can be explained differently based on the first halacha of the Rambam's Hilchos Talmud Torah: "Women, slaves, and children (ketanim) are exempted from Talmud Torah, but a father is commanded to teach his young child (katan) Torah." Two questions can be raised. First, why does the Rambam mention only a katan? Isn't a father required to teach his son after Bar-Mitzvah? Second, why does the Rambam begin with an exemption? Wouldn't it be more logical to state the obligation before the exemption?
It would seem that according to the Rambam , one cannot be commanded to teach someone who himself is obligated to learn. Therefore, it is necessary to mention the fact that ketanim are exempt from talmud torah before stating the obligation of the father to teach him. While a father is certainly responsible for his son's education beyond Bar-Mitzvah, this obligation does not fall under the specific mitzvah of teaching. (Velimadtem. Compare Chazon Ish Y.D. 152:1).
In this light, the bracha is the father's statement of gratitude that he has completed his mitzvah of velimadtem and is no longer punishable for it. This interpretation is supported by the context of the bracha's midrashic source.: A father must care for his son for thirteen years, after which the son himself must choose the tents of study over the hunting field. Since velimadtem does not apply to daughters or mothers, the bracha is not needed for or by them.
The Magen Avraham (ibid:4), citing the Zohar, requires that a father make a festive meal when his son becomes Bar-Mitzvah just as he makes for his son's wedding. The Machtzes Hashekel (op.cit) equates this with the Maharshal's view that a Bar-Mitzvah seudah celebrates the boy's becoming commanded to do mitzvot (metzuveh veoseh Sec B.K. 87a). This equation is questionable, for it seems that while the Maharshal requires the son to celebrate , the Zohar's obligation relates to the father. The Zohar's comparison to a wedding reflects a father's mitzvah to celebrate whenever he has completed one of his obligations towards his son, namely milah, pidyon haben, teaching him Torah and marrying him off (Kiddushin 29a).
This analysis leads to a compromise view concerning Bat-Mitzvah celebrations. The Yechaveh Daas (II, 29), citing the Maharshal's reasoning, which applies equally to girls, equates Bar and Bat-Mitzvahs. Igros Moshe (O.C. I.104: II,97) states that a Bat-Mitzvah party is not a seudat mitzvah at all. It would seem that the Maharshal's reason does, in fact, apply and therefore the girl is required to make a party for her close friends and family. However, a wedding-like feast, which reflects the completion of the father's obligation of velimadtem, applies, like the bracha of Baruch shepetarani, to a Bar-Mitzvah only.