My Friend: SJS is right. Shulchan Aruch discusses a Father’s obligation to teach his children Torah; in other words, teaching a young child w/o his/her consents. However, a girl on her own may learn Torah Shbaal Peh and she receives schar as stated explicitly in the S”A at the beginning of that same se’if. According to your [mis]understanding, the S”A would be contradictory in the same se’if.
Do you not know that Rav Isser Zalmen Meltzer’s rebbitzin wrote the sefer Even Ha’azil for her husband?