Not mentioned in one of my earlier posts while in New Orleans, was that after שחרית (morning prayer service) that day, the Chabad rabbi went around asking if anybody wanted to put on תפילין (tefillin), as there were some college students around, some of whom had just arrived for breakfast and who hadn't davened (prayed) yet. While going around, my sister said she would, but that's not for what the rabbi was asking. She further noted that he had been asking if "anybody" wanted to put on tefillin, though she pointed out that he ought to be saying "any men", since he probably wasn't going to give it to any women (for more on Chabad's perspective and discourse on women not wearing tefillin, see askmoses.com). I then offered my sister mine, which was met by her response that she's not going to put on tefillin until she knows more about the subject. Thus this posting (I am not here dealing with the issue of girls putting on tefillin in school, but rather women in general.).
The discussion largely begins with a mishnah in the third chapter of Berakhot:
The reason that they are exempt is due to their exemption from all positive time-bound commandments (as they are worn neither on shabbas nor on holidays, there is a time element to them), which would mean that it's not that they are forbidden to perform such מצות (commandments), but that they don't have to [and can perform them if they so choose].נשים ועבדים וקטנים--פטורין מקרית שמע ומן התפילין, וחייבין בתפילה ובמזוזה ובברכת המזון.Women, servants, and children are exempt from the reading out of the Shema and from [wearing of] tefillin, but are obligated with prayer, mezuza, and with the grace after meals.
The main argument that was put forth against women putting on תפילין (tefillin) is that put forth by the sixteenth century sage Rabbi Yosef Karo (in his Beit Yosef) (and the Tosafist(s) that he quotes):
Where the idea comes that is mentioned in the Tosafot that women are not careful about having a clean body is quite strange. In our times, women are cleaner than men; if anything, it should be that men are not careful enough to keep clean bodies (!). Thus, how can one say that women cannot wear tefillin due to lack of bodily cleanliness?בית יוסף אורח חיים סימן לחA mishneh in chapter "Who's dead..." (ch. 3 in Berakhot), the [stam] gemarra (Berakhot 20a) gives the reason that it's because it's a positive time-bound commandment, and women are exempt from all positive time-bound commandments. And Rabbi Asher, son of Yehiel wrote in the laws of tefillin (section 29): "Even though we have established like Rabbi Akiva, who said, 'Night is a time of tefillin' (Eruvin 96a), shabbasos and holidays are not times of tefillin. [The author of the] Kol Bo wrote (in section 21) in the name of the Ram (?), 'that if women want to put on tefillin, we don't listen to them because they don't know how to guard themselves in cleanliness.'" And in the book Orhot Hayyim (laws of tefillin, section 3), asks on what is said in the beginning of the chapter "The one who takes out tefillin..." (also on Eruvin 96a) that 'Mikhal, daughter of Kushi, wore tefillin and the sages did not reprimand her.' And to me it seems that the reason of the Ram is like the Tosafot have written (Eruvin 96a, s.v. "Mikhal") that in the Pesikta [Rabbati] (chapter 23) that the sages did reprimand her. And they (the Tosafists) explain that the reason is that [wearing] tefillin requires [one to have] a clean body, but women are not zealous to be careful. And the Ram wanted to suspect [to be careful] to the words of the Pesikta.
ונשים ועבדים פטורים. משנה בפרק מי שמתו (ברכות כ.) ויהיב טעמא בגמרא משום דהוי מצות עשה שהזמן גרמא וכל מצות עשה שהזמן גרמא נשים פטורות. וכתב הרא"ש בהלכות תפילין (סי' כט) ואע"ג דקיי"ל כרבי עקיבא דאמר (עירובין צו.) לילה זמן תפילין מכל מקום שבת ויום טוב לאו זמן תפילין: כתב הכל בו (סי' כא) בשם הר"ם שאם רצו הנשים להניח תפילין אין שומעין להן מפני שאינן יודעות לשמור עצמן בנקיות עכ"ל ובספר ארחות חיים (הל' תפילין סי' ג) הקשה עליו מדאמרינן בריש פרק המוצא תפילין (שם) דמיכל בת כושי (פירוש בת שאול) היתה מנחת תפילין ולא מיחו בה חכמים. ולי נראה שטעם הר"ם כמו שכתבו התוספות (ד"ה מיכל) דאיתא בפסיקתא (רבתי פרק כב) שמיחו בה חכמים ופירשו הם דטעמא משום דתפילין צריכין גוף נקי ונשים אינן זריזות ליזהר והר"מ רצה לחוש לדברי הפסיקתא:
Nevertheless, in his Shulhan Arukh, he didn't try to prevent women from wearing them (OC 38.3: "Women and servants are exempt from [wearing] tefillin, because they it is a positive time-bound commandment."), only saying that they were exempt from wearing them. However, his contemporary, Rabbi Moses Isserles, glossed there that "but if women want to be stringent upon themselves, we reprimand them."
As to why Rabbi Isserles opined in such a fashion, it seems that it was due to the cleanliness concern (see the ט"ז, מ"א, & מ"ב who all opine that that was his reasoning). However, the wording of stringency pointed to as being the reason that women ought to be reprimanded seems like the crux of the issue for Rabbi Isserles. It may be due to the concern that if women think that the wearing of it is a stringency, that it is an erroneous line of thinking.
Alternatively, it seems that there is a cultural concern here. Such that, halakhically, it's fine to do a מצוה (commandment), however, it strikes men in such a way that it just doesn't jive with their sense of society (this was briefly brought up in On the Main Line). This is largely similar to the idea that tefillin and tzitzis are distinctly men's garments, which is an interesting argument (keep in mind the famous aphorism that "Clothes make the man," thus indicating that clothing is a social marker, and that it is something that is culturally-contingent), though according to the Bible, that is not so - it is only through rabbinic midrash that one learns of women's exemption from these commandments, but neither their inability to perform them, nor of their sense of being garments singled out for men only (if one even sees tefillin as being a garment in the Torah, but that's not important for this discussion).
Nevertheless, I think it's important to be sensitive to one's environment (yes, this concept arose in my mind through the conversations we had about women and tefillin in yeshiva). If one is in a place where it makes people (not just men, maybe also women) uncomfortable or is against the customs or comfortability of a place, it may be an issue to the extant that it is not something to which people are accustomed and be a statement of some sort with which those people or places are not okay.
So, I think I would say that it would be okay for her to wear tefillin if she wanted to, though she ought to be careful at Chabad, as it may go against their understanding of gender distinctions.
(A couple of blog postings are worth a read on this topic: On The Fringe and Barefoot Jewess.)