Answer: The Torah (Devarim 22) states: “A man’s vestment shall not be on a woman and a man shall not wear a woman’s vestment.” This teaches us that a man may not wear women’s clothing and a woman may not wear men’s clothing.
The Gemara in Masechet Nazir (59a) states: “Rabbi Eliezer ben Yaakov says: From where do we learn that a woman may not go out to war with a weapon? This is derived from the verse, ‘A man’s vestments shall not be on a woman and a man shall not wear a woman’s vestments.’”
The Rambam (Chapter 12 of Hilchot Avodah Zara, Halacha 10) states: “A woman may not wear a man’s vestments, such as putting a (man’s) turban or hat on her head or wearing armor and the like. A man may likewise not adorn himself with women’s vestments, such as wearing colorful clothing or gold chains in a place where only women do so; this is all relative to the custom in one’s specific place. A man who wears women’s vestments or a woman who wears men’s vestments is liable for lashes.” Maran writes in his Kesef Mishneh (Maran’s commentary on the Rambam’s Mishneh Torah) that the Rambam intends to rule in accordance with the view of Rabbi Eliezer ben Yaakov, for the Gemara in Masechet Gittin (67a) states that the teachings of Rabbi Eliezer ben Yaakov are “few but clean” (meaning that the Halacha follows all of his rulings). Other Rishonim rule likewise. The Tur and Maran HaShulchan Aruch rule accordingly (Yoreh De’ah, Chapter 182, Section 5) based on the aforementioned Rambam.
Nevertheless, it is clear from the wording of the Rambam and the Poskim that anything which women wear as well, although it may be a men’s garment, there is not prohibition for women to wear it. The opposite is true as well: Regarding something which was originally a practice of women after which men began doing the same, there is no prohibition to do it.
An example of this is looking in a mirror. According to our Sages, a man may not look in a mirror in order to put himself together. However, in our times, men customarily look in the mirror as well; thus, this is no longer prohibited in our times since the reality of the matter has changed and this is no longer strictly a feminine practice.
Regarding our question about weapons, although weapons are usually made more for men than for women, nevertheless, when there is an essential need to carry a weapon, such as in border communities in Israel where there is always fear that murderous terrorists will strike and cause much destruction and bloodshed, women may in fact train with and carry weapons in order to protect themselves and the school-children in their care, for nothing stands in the face of a life-threatening situation.
Indeed, Rabbeinu Yehuda Ha’Chassid writes in his Sefer Chassidim (Chapter 200): “There are certain times when one must act against the Torah in the name of Hashem. Thus, if enemies have occupied a Jewish city where women walk around and they are afraid of being caught and assaulted by these enemies, they may dress themselves in men’s clothing and arm themselves with swords in order to trick the enemy into thinking they are men. The same holds true for young men without a beard that they may dress up in women’s garments in order to protect themselves from the enemy.” The Terumat Ha’Deshen (Chapter 196) rules likewise.
Maran Rabbeinu Ovadia Yosef zt”l (in his Responsa Yechave Da’at, Volume 5, Chapter 55), Hagaon Harav Moshe Feinstein zt”l (in his Igrot Moshe, Yoreh De’ah, Volume 6, Chapter 35), and many other great Poskim rule likewise. They quote other sources for leniency in this matter as well.
Summary: Female school-teachers in border towns (primarily in Israel) may train with and carry weapons while guarding the school. They must nevertheless adhere strictly to the rules of modesty appropriate for Jewish women while training and they may not be secluded with a man during the training operations, based on the rulings of the Tur and Maran Ha’Shulchan Aruch in Even Ha’Ezer, Chapter 22. May Hashem protect their comings and goings forever, Amen.