Answer: The Rema (OC 225:2) writes that when one’s son becomes bar mitzva, his father recites baruch sheptarani meonsho shel zeh, (Blessed is He who exempted me from this one’s punishment). The Magen Avraham (OC 225:5) and Mishna Berura (225:7) explain that as the father is obligated to educate his son, he is responsible for his son’s misdeeds, too. The son is responsible for himself upon turning bar mitzva. Thus, his father recites this beracha upon being released from this obligation.
As the obligation to educate one’s sons in learning Torah does not apply equally to girls (Nazir 29a), the Pri Megadim (Eishel Avraham 225:5) writes that this is one of the reasons why parents don’t say baruch sheptarani on their daughter’s bas mitzva. The Kaf Hachaim (OC 225:15) adds that as girls typically stay at home and are supported by their parents until they marry, their parents are more likely to continue educating them even after their bas mitzva.
R’ Moshe Feinstein (Igros Moshe OC 2:97) writes that while there is an equal simcha with one’s daughter becoming bas mitzva as there is for one’s son turning bar mitzva, the change in a girl’s status is not as obvious as a boy who is now included in a minyan, etc. In the last teshuva that R’ Moshe wrote (ibid. OC 5:14), he adds that this beracha is specifically said when a bar mitzva boy gets his aliya (See Rivevos Ephraim 4:44:40; 5:464:2; 7:59; 7:71).
The Magen Avraham, however, quotes the Levush (OC 225) who writes that the reason for this beracha is because the father is relieved that his adult son will no longer be punished as a result of his father’s misdeeds. Accordingly, some suggest that the bar mitzva boy says this beracha rather than his father. R’ Baruch Epstein (Baruch Sheamar, Tefilla p189) questions whether according to this, girls should say it, too.
Likewise, R’ Ovadia Yosef (Yabia Omer OC 6:29) argues that while girls don’t have all the same obligations as boys, their parents are still required to educate them. According to this Levush, one would recite this beracha on one’s daughter’s bas mitzva, too.
In conclusion, while some sefardim say baruch sheptarani on their daughter’s bas mitzva, it isn’t said in ashkenazi shuls.