Why the Shechinah? There are two aspects to consider. First, along with Chochmah, the Shechinah represents the feminine aspect of G-d (as we understand it; obviously G-d transcends gender but we understand things in concrete ways). This is alluded to in the brachah Bilam inadvertently gives the Jews, "Mah tovu," "How good are your tents," which we are taught actually refers not to a metaphor (unless you go to the Kabbalah, but that's another discussion of course) but to the actual physical tents of the Jews in their camps in the deserts, for the women's inherent modesty made them always site their tents so that no entrance or opening faced directly to those of another tent; in this way they always had privacy and provided it to their neighbors. This true modesty is one of the greatest traits of the Jews, and das Yehudis has always been a closely guarded value.
|Summertime! And being a Jewish girl is great!|
In addition the Shechinah itself was found in the Mishkan itself, inhabiting the Kodesh Kodeshim. The karbanos, tefillos, and study of the Jews was their very protection as the Shechinah kept them from harm.
In the end, it was indeed mostly men who sinned following Balak and Bilam's campaign, but the women and their holiness were able to protect the people as a whole and it was their feminine nature, their holiness, their prayers, which kept G-d from destroying the people entirely.
We must continue today in this vein; remembering our natural modesty (without going overboard or being judgmental of others' standards of modesty) in our dress, behavior, demeanor, and thought. Yet that alone is not enough; we all must continue our tefillos and talmud Torah as well as the other mitzvahs we can perform to bring about protection for the Jewish people as a whole.