Recently, there was a controversial decision of Salanter Akiba Riverdale (SAR), a Modern Orthodox day school, allowing female students to wear tefillin (commonly translated as "phylacteries"; תפילין). While SAR is not the first yeshiva to allow this, SAR's actions nevertheless caused an uproar. If this isn't anything unprecedented, why the hullabaloo? Is a woman donning תפילין a violation of Jewish law?
The origin of the exemption of a woman from donning תפילין is the Mishnah (Berachot 3:3). The basis for this exemption is the notion that donning תפילין is a מצוה עשה שהזמן גרמא (time-bound, positive mitzvah), from which women are exempt. Interestingly enough, we see enough exceptions to this rule. Targum Yonatan ben Uziel, an ancient Midrashic, Aramaic translation of the Torah, viewed donning תפילין as a form of cross-dressing. Some agreed with this theory, but most halachic decisors rejected this notion because תפילין is not considered clothing. Another objection is due to the concern of having a pure body, or a גוף נקי (Piskei Riaz RH 4:3). With respects to גוף נקי, Rambam ruled (Hilchot Tzitzit 3:14) that the impure, like those who are ritualistically pure, are required to don תפילין. Also, words of Torah were not susceptible to טמאה (Berachot 22a), which means that נדה would not be an issue. Within the context of תפילין, the Talmud (Shabbat 49a) defines גוף נקי as flatulence, which is not limited to women. It can be easily argued that גוף נקי is not a sound basis for prohibiting women from donning תפילין.
Although one is exempt, this does not automatically mean that a woman is prohibited, either. The Talmud (Eruvin 96a) states that "Michal, the daughter of King Saul, used to don תפילין and no one protested." Even with this example, normative practice has been that women are not to don תפילין (Rema, Shulchan Aruch, Orach Chayim, 38:3).
In spite of the Rema's ruling, there is plenty of precedent allowing for women to don תפילין. Rambam (Hilchot Tzitzit 3:9) ruled that women can don תפילין, but did not recite the bracha because the phrase "אשר קדשנו במצותיו" would not apply [to those who were not commanded to do a mitzvah]. Sefer HaChinuch (Mitzvah #421) rules under a similar vein, by saying that a woman is not obligated to don תפילין because it's a time-bound, positive mitzvah, but if she wants to, there is no objection. The Tosafot agrees with the permissibility, but disagrees with the "אשר קדשנו במצותיו" part (Tosafot, Ran RH 33a). In addition to Rabbeinu Tam and Rabbi Zerahia HaLevi, Rabbi Moshe ben Yaakov of Coucy also agreed with allow for donning תפילין to be permissible and optional for women (Hagahot Maimoniyot Tziztit 3:9).
If a woman is donning תפילין because she wants to act like a man or "stick it to the Man," then the intention is not pure, and I would have a problem with that. Conversely, I have never seen anyone question a man's intentions of donning תפילין that were solely based on his gender, which I find all the more odd because it is my understanding that traditional Judaism claims [at least in theory] that women to be on a higher spiritual plane than men, hence why it's one of the reasons why they are not obligated to perform the mitzvah of donning תפילין. Even so, the Rashba stated that a female who desires to don תפילין to fulfill a g-dly commandant, a woman can use Michal bat Saul as an example to justify the donning. If it is ruled permissible by prominent rabbis, there is no harm in a woman performing the mitzvah, especially when it is more laudable for someone to do a mitzvah voluntarily than one who is commanded to do so (Bava Kama 38a, 87a).
Views on women have changed drastically enough over time, which has the ability to alter halacha, or at the very least, our perceptions thereof. The Jerusalem Talmud (Berachot 2:3) forbids donning תפילין because it is a form of studying Torah, from which women traditionally had been banned. If this is true, then the prohibition should have been lifted in 1917 when the Bais Yaakov movement was born and subsequently allowed women to study Torah. Aside from the Bais Yaakov movement, women were permitted to study Talmud in the latter half of the twentieth century. If the reason for not allowing women to don תפילין is because of a link between Talmud Torah and תפילין, then the link is severable.
Progress in the arena of "Judaism and women" goes beyond studying Torah. Take the recent development of the bat mitzvah ceremony. In even more recent times, R. Avi Weiss ordained three women to be a maharat, which is a religious leader that is comparable to being a rabbi. Furthermore, the idea of partnership minyanim is highly contentious. Other debates being hashed out are whether women can read from the Torah, dance with the Torah, or start a women's tefillah group.
When you view the issue through the lens of sociology and religious politics, as opposed to the halacha itself, the contention is threefold: 1) too much change is taking place too quickly, which violates the preservationist mentality of the modern-day Orthodox establishment that fears the slippery slope over the minutest change, 2) women are being shown enough inclusion where it irks a sizable amount of influential individuals, especially those who would rather not see women empowered and 3) since many consider donning תפילין to be "a man's mitzvah," this will be seen as a further blurring of gender roles, which is problematic for the Orthodox because Orthodoxy has very rigid gender roles.
Religious politics set aside, the halacha is pretty clear on the issue. Although it was not a practice of the vast majority of Jewish women to don תפילין and women are not technically obligated to don תפילין, there is legal precedent for permitting women if they choose to do so. If a woman finds that donning תפילין brings her closer to G-d and makes her a better Jew, we should encourage her to perform more mitzvahs, not less. We should encourage her to find spiritual meaning in her Jewish practice.
The reason why women and תפילין has been so contentious is because those in the Orthodox world are reaching a crossroads, a crossroads in which the leaders of Orthodoxy have to decide how they will view gender roles. Some Orthodox Jews want to maintain rigid, stringent gender roles in which a woman's role is to procreate, tend to the needs of the children, and take care of the house. Other Orthodox Jews do not view the topic as bifurcated as the ultra-Orthodox do. The issue of women donning תפילין is a case study of said divisiveness (As a brief side note, the issue of "Judaism and homosexuality" touches upon the gender bifurcation as much as "Judaism and women," which is why they are two exceptionally hot-button issues in the Orthodox world). As schismatic as the topic of gender might be, the extent of disagreement will shape the direction in which "mainstream Orthodoxy" heads. Will Orthodoxy as a whole continue to view women as mere baby-makers, or will Orthodoxy create a venue in which women can also fulfill their spiritual need to connect to G-d?