According to R. Meir of Rottenberg (as quoted by his disciple, R. Shimshon bar Tzadok), women are exempt from laying tefillin because it is a positive, time-bound mitzvah since tefillin are not worn on Shabbat. However, “one should not protest against their wrapping themselves in tzizit and reciting the blessing because they can accept upon themselves an obligation.” He goes on to cite Kiddushin 31a, where the Gemara states, “Greater is he who is commanded and performs mitzvot than he who is not commanded.”
According to Sefer Hachinuch, “This mitzvah applies at all times and in all places for men, but not for women because it is a time-bound positive mitzvah. However, if [women] want to put on tefillin, we do not object and they receive spiritual reward.” Still, the prevalent custom has been that women do not don tefillin.
“Women … are exempt from tefillin because it is a positive time-bound mitzvah,” states the Shulchan Aruch (38, 3). The Rema adds, “And even if women want to be strict with themselves [and put on tefillin], we object to this practice.”
Women’s exemption alone would not necessarily be grounds for objecting to isolated incidences of them wearing tefillin. Women are in fact usually encouraged to perform even those mitzvahs from which they are exempt, such as lulav and sukkah. In his book Jewish Women in Jewish Law, Rabbi Moshe Meiselman explains that women are discouraged from optionally wearing tefillin, just as men are discouraged from wearing them any longer than necessary.
Although “the basic mitzvah of tefillin is that they be worn all day, only people of unusual sanctity, like the Vilna Gaon, did in fact do so … Men wear them, generally, only during prayer, the minimal period of time required. Similarly, although we begin training children to perform mitzvot far in advance of maturity, tefillin are not worn until shortly before Bar Mitzvah. The optional wearing of tefillin is to be avoided! Those who are obligated cannot be prevented from performing [the mitzvah of tefillin], but the rabbis [in the Talmud] debated the propriety of [its] performance by anyone on an optional basis, weighing the positive results against the possible negative results. The debate in the Talmud on whether women may wear tefillin is concerned with this very point.”
The consensus opinion in Jewish law is that the very sanctity of tefillin demand that they be worn on an as-needed basis only.
The kabbalists explain that women do not need the mitzvah of tefillin as men do, because women have innate ways of binding with God and the tefillin’s component parts correspond with unique female qualities: the tefillin’s hollow chamber corresponds to the womb and the tefillin straps correspond to the umbilical cord.
According to some legends, Rashi’s daughters laid tefillin regularly.
If a woman does decide to lay tefillin, it should be done in private, not ostentatiously or as a political statement. In any case, a woman who wants to wear tefillin should weigh the matter carefully and be sure she is doing it for the right reasons. A good place to start reading would be Why I Don’t Put on Tefillin or The Wall is Wailing.