The Rambam begins hilchos talmud Torah with the following halacha: Women and slaves are exempt from talmud Torah. A man is obligated to teach his son Torah, as it says, “velimadetem osam es beneichem ledaber bam.” However, a woman is not obligated to teach her son Torah because whoever is obligated to learn is obligated to teach – and since a woman is not obligated to learn, she is not obligated to teach.
The Shulchan Aruch (Orach Chaim 47:14) says that women should recite birchas haTorah. There is a machlokes Rishonim whether women can recite a berachah on a mitzvah from which they are exempt from performing. According to the Rishonim who opine that they can recite a berachah, we understand that they can recite the berachah on Torah as well. But the Mechaber (of the Shulchan Aruch) rules in favor of those Rishonim who do not permit women to recite a berachah on a mitzvah from which they are exempt. How then can he rule that they should recite a berachah on the mitzvah of learning Torah, since they are exempt from it?
The Magen Avraham quotes the Beis Yosef, in the name of the Agur, and explains that women are obligated to learn the halachos that pertain to them and are obligated to say korbanos, just as they are obligated to daven. Thus they may recite the berachah on Torah. The Magen Avraham also explains that it is for this reason that women can mention in the second berachah of bentching, “v’al Torasecha she’limaditanu,” since they are obligated to learn the halachos that pertain to them.
The Vilna Gaon does not agree with the Magen Avraham’s suggested answer, since the Gemara derives from the pasuk, “velimadetem osam es beneichem” – v’lo benoseichem – that women are exempt from the mitzvah entirely. This even regards learning about the mitzvos that they are obligated to perform.
Reb Shach, in his sefer on the Rambam, explains that there are two obligations to learn Torah. One is the general mitzvah to learn the entire Torah. This mitzvah is derived from the pasukim of “veshinantam” or “velimadetam.” It is from this obligation that women are exempt. However, there is another obligation to learn Torah that is a component of every mitzvah individually, demanding that one learn how to perform that particular mitzvah. Included in the commandment to perform each mitzvah is an obligation to learn how to properly perform that mitzvah. The obligation to learn how to perform the mitzvos is also a mitzvah of learning Torah.
Women are only exempt from the general mitzvah of learning the entire Torah. But they are obligated to learn how to perform the mitzvos for which they are obligated to perform, and that too is a mitzvah of talmud Torah. Hence they can recite the berachah on the mitzvah of talmud Torah, even according to the opinion that women may not recite a berachah on a mitzvah for which they are exempt.
Reb Shach brings a proof from a Tosafos in Avodah Zarah 3a that this obligation (to learn how to perform the mitzvos that you are obligated in) is a mitzvah of talmud Torah. The Gemara there says that a non-Jew who learns Torah is comparable to a kohen gadol, and he is rewarded just as one who is not obligated to perform the mitzvah (which is a lesser reward than one who performs a mitzvah that he was obligated to carry out). Tosafos explains that the Gemara is referring to a non-Jew who learns Torah that pertains to the seven obligatory mitzvos that non-Jews are required to perform. (A non-Jew is not allowed to learn any of the other parts of the Torah.) If learning the halachos of how to properly perform a mitzvah is not considered a mitzvah of talmud Torah, why does the Gemara make reference to a non-Jew who learns Torah? The Gemara should have said this: a non-Jew who is involved in preparing for a mitzvah that he is obligated to do (i.e. he kills an animal so that it is not eiver min ha’chai.) One can infer from this that there is an obligation to learn the halachos of each mitzvah, and that that is a mitzvah of talmud Torah.
