Why do we need minimum 10 men for a minyan?

This question breaks into two: 1. What is the source? 2? What is the reason or message? The source of the idea of ten for a minyan comes from the verse (Vayikra 22;32) "I (G-d) shall be santified in the midst of Israel". The Talmud (Brechot 21b) explains that the term "in the midst" refers to at least ten people. Sanctified refers to both the obligation to sanctify G-ds name by adhering to His commandments even under duress, and to the recitation of prayers that are sanctifications of His name, like the Kaddish,Kedusha and Barchu. The idea seems to be that Certain forms of the sanctification of G-d's name can only come about within the framework of the community of Israel. Ten men represent a microcosm of that community. A minyan is a symbolic representation of the Jewish people. Women are not counted for a minyan in halacha. I believe that the explanation is that a woman is not a representation of community. Each woman herself is a determiner of Jewish identity. We have matrilineal descent, which means that a person born of a Jewish mother is Jewish, eeven if the father is not Jewish, while a Jewish father does not make the baby Jewish if the mother is not Jewish. A womans identity is personal and does not require communal representation.