“Rachel,” is the younger sister "הקטנה ", who corresponds to the garments of speech and action, which are two aspects of Malchus (the “smaller” letter "ה"), and is connected to the Oral Torah, which is derived from the Written Torah. When the Oral Torah explains how to fulfill the Mitzvos, these explanations are all based on verses from the Written Torah. This corresponds to the idea that the letters of speech come from the letters of thought, since a person can only speak about something that he thought about first. Thus, just as speech comes fro thought, the Oral Torah (which is conveyed through speech) comes from the Written Torah (which respresents the Torah as it exists in Hashem’s Thought).
Now, the maamar will continue to explain why these two aspects of Leah and Rachel require the revelation of “the Intellect of the Father:”
Revelation of the Intellect of the Father
And therefore, the creation of these two aspects [Leah and Rachel] is drawn forth specifically through the revelation of “the Intellect of the Father,” since this is the idea of self- nullification, from which comes the idea of “returning” to the world, which is the idea of drawing down G-dliness in the vessels and letters of the performance of the Mitzvos in thought, speech, and deed, which are the aspects of Leah and Rachel,
In other words, when a person submits to Hashem’s Ultimate Truth by employing the “Intellect of the Father,” he does not leave the world, but, instead becomes empowered to fulfill his mission of revealing Hashem in the world by way of the words of Torah (on the levels of both thought and speech) and the fulfillment of the Mitzvos. Thus, the creation and completion of the garments (represented by Leah and Rachel) are specifically through revealing “the Intellect of the Father.”
Why the Intellect of the Mother is Not Sufficient
This is not the case with the aspect of “the Intellect of the Mother.” from which comes the yearning to leave the world and be included in the truth of Hashem, since the exact opposite effect occurs, where the person wants to leave the vessels and the letters, since he wants to leave the limitation of the physical world altogether.
In other words, if a person comes to a deep understanding of the infinite greatness of Hashem and how all the worlds are less than one thought compared to the vastness of the soul, then a person will want to leave the limitations of the world and all of the “vessels” and letters of the Torah, which are expressed in physical matters (all of the Mitzvos are specifically in physical matters), in order to be able to enter the limitless truth of Hashem’s greatness. In such a case, however, he would leave behind the garments of Torah and Mitzvos, G-d forbid, thus neglecting the ultimate desire of Hashem. This is why understanding Hashem’s greatness is not sufficient; there must be recognition and “seeing” that we are standing before the King who sent us here on a mission, and our entire existence is to fulfill that mission, as we explained.