In response someone (presumably a man) wrote, that all things being equal we find no source in Halacha for a woman to be given preference over a man or vice versa, and therefore chivalry has no place amongst Frum Jews. Regarding her complaint that she found herself falling on male passengers; he responded that having men standing and falling on female passengers is not a better alternative.
I would like to express my feelings on the matter.
Firstly, contrary to the second letter-writer’s statement we actually do find instances of chivalry in Halacha.
The Mishnah in Horios (13a) states that in regard to sustaining and returning lost objects one should service a man first, whilst in regards to clothing and rescuing, a woman would take precedence. (The Beis Yosef (YD 251) explains that when the Mishnah mentions “sustaining”, it refers to saving lives and in this a man comes before a woman, however in regards to charity a woman takes priority similar to the Halacha that she takes priority in receiving clothing.)
Furthermore the Gemorah states (Brachos 61a & Eiruvin 18b) that if a man and woman simultaneously reach a narrow passageway the man should go first since it is improper for him to walk behind a woman. The Gemorah then adds that this Halacha applies even to a husband and wife, and Rashi (Eiruvin ibid.) explains since it is unbecoming for a husband to walk behind his wife.
It is quite clear that there exist Halachos mandating whether and when, a man or woman take precedence.
Also, the letter-writer fails to realize that with all societal chivalry aside, Mentchlichkeit is a basic and far-reaching Halacha. Without unnecessarily going into details, everyone understands that most women could use a seat more than the average man. Therefore basic human decency suggests that a man relinquish his seat in favor of a woman. Being a Mentch and interacting with society in a fine and decent manner, is understood to be included in the adage of Derech Eretz Kodmah LaTorah.
As for his point that having men standing and falling on top of women is just as severe a breach in Tznius; what he fails to recognize is that for whatever the reason the male passengers usually greatly outnumber the female passengers on these Frum busses. Having some men stand would generally not lead to men falling on seated women as these men can, and should, stand between seated men. Women, on the other hand, if left standing will generally find themselves standing between men which could lead to un-Tzniusdik results.
If one would only be aware of the true situation, one would realize that the woman’s complaint was valid; not necessarily from the standpoint of chivalry but from the standpoint of Mentchlichkeit & Tznius.