A general principle in Judaism is that women are not bound by time-bound, positive commandments. Tefillin fall in to this category as a time-bound, positive commandment.
In addition, it is a Torah prohibition for women to wear garments that are made specifically for men (see Deuteronomy 22:5). Yonatan Ben Uziel is a Talmudic Sage who translated the Bible in to Aramaic and he explained this verse as referring to Tefillin and Tzitzit. According to this opinion, a woman who wears Tefillin or Tzitzit is therefore breaking a Torah law.
Rabbi Aryeh Kaplan , a modern scholar (1934-1983), explained that women actually have the commandment of Tefillin naturally incorporated in their spiritual makeup and therefore have no need to wear them. An interesting development of this idea is based on the fact that the purpose of the commandments are to establish a link with G-d, with resembling Him being the most profound way to do so.
Women have a unique way that they resemble G-d that men will never have- women can create within her body. It is only women who can bear children and in this way women are most closely connected to G-d’s attributes than man.
Two basic elements in Judaism are the home and the synagogue (the Jewish house of prayer). In other religions the house of prayer is the primary element in the religion. Judaism is unique in the way that the house and house of prayer are viewed on equal levels.
Many of the most important rituals are performed exclusively in the home, such as the Passover Seder, the Sukkah, the Shabbat meals and the Chanukah Menorah. Judaism’s continuity is dependent on that which goes on in the Jewish home.
In Hebrew the word for home is Bayit and it is not by chance that the box of a Tefillin is known by the very same name. Men have their Bayit- their Tefillin and women have their Bayit- the home in which they raise their families.