A standard answer to the question "why aren’t women obligated in all the commandments?" is that women experience through their physical bodies (cycles, etc.) whatever it is the Mitzvah is supposed to elicit in men, and therefore don’t need to perform those Mitzvahs externally. Is there a source or text (Hebrew or English) that goes through this and correlates the two? I mean describes the Mitzvah, what it is supposed to accomplish, how the action of the Mitzvah accomplishes this for men, and how this is manifested in women already.

A more accurate understanding is that just as there are Cohanim, Leviim and Yisraelim etc., each group with certain laws that pertain specifically to them as together they make up the unity of the Jewish People, so too there are different commandments for men and women. Men and women are different, complementing each other to form a single unity; each is not a unity unto himself. It would be incorrect therefore to assume that the goal for men and the goal for women is identical; they are not identical- they are complementary, together comprising the spiritual completeness of Man. One can try to understand from the difference in Mitzvot between men and women what different role is played by each in achieving the completeness of the whole.