Men owe women Chivalry unconditionally because society works better under that principle. I tend to phrase things saying Chivalry is “God’s will” or a “God imposed duty upon men on behalf of women” but what this really boils down to is a utilitarian argument that Chivalry makes society work. Chivalry broadly defined is foundational to society and foundational to good relations between men and women. You must understand that women are vulnerable to men and that women must trust men in order for men to be able to serve women as they should. To require another’s assistance makes the person needing assistance vulnerable to the person providing assistance as the person who needs assistance will be in bad shape if the provider of assistance fails to provide. Men are the providers of assistance while women are the receivers of assistance; this then makes women vulnerable to men. Society needs for women to make themselves vulnerable to men voluntarily so that men can serve women so that women can serve children. This then creates a requirement for men to be seen as trustworthy in women’s eyes. Universal Chivalry then is the mechanism by which men collectively establish themselves as trustworthy in general in women’s eyes. As a man it is desirable for women to have a baseline of positive associations and trust regarding men in general; in other words it benefits all men if women in general trust men in general. This generalized assumption of trust in men can only be established through a generalized or unconditional imposition of Chivalry upon each individual man by men collectively. This is the purpose unconditional Chivalry serves.
From the point of view of the Chivalrous man the un-Chivalrous man is a parasite and free loader because he is taking advantage of the trust Chivalrous men have created but in return is destroying trust in Chivalrous men by his own selfish un-Chivalrous acts which put all men in a bad light. This then is the basis of Chivalrous men punishing un-Chivalrous men for their violation of the male Chivalrous code. You can view Chivalry as a male code of honor whose purpose is to benefit men by making men trustworthy in women’s eyes. The un-Chivalrous man is then undermining the male code of honor which harms all men’s reputation thereby harming all men which then motivates the punishment of the un-Chivalrous man for his violation of the male honor code. Through this mechanism the male code of honor is sustained leading to men being Chivalrous in general leading to women trusting men in general leading to a well functioning society and good relations between men and women.
On the specific issue of “men dying for random women” such as in the extraordinary circumstance of being on a sinking ship with not enough lifeboats; this falls under the category of community Chivalry. I have put Chivalry into three categories; romantic Chivalry, community Chivalry, and public policy Chivalry. Community Chivalry is where men provide for and protect “random women” or women they are part of the same community with. Let’s focus on a hypothetical. A man and a woman are on a sinking ship; two people but only one lifeboat. One will die and one will live; that is the cold hard facts. What shall be done? Option one; man says “I’m stronger than you” and pushes woman into the water and climbs safely onto the lifeboat. Option two; man says “I’ll flip a coin; heads you die, tails I die.” Option three; woman proclaims “You man are the stronger and the stronger shall prevail” and so jumps into the water heroically sacrificing her life on behalf of the man. Option four; man proclaims “As a man it is my duty to provide for and protect woman; the only thing I can do to protect you is sacrifice the lifeboat to you, this is my last act of love for womankind” and jumps into the water heroically sacrificing himself for the woman.
Which of these four options is the best for society? There is no question; by far option four is the best for society. From the point of view of society one will die and one will live; the man and the woman have equal value as human beings so either one dying is equally bad. The moral question at stake is not whose life is more valuable because each life is taken to have equal value; the moral question is the wider meaning of the death that occurs. In option one the man simply shoves the woman into the water saving himself. There is no redeeming virtue in this; it sends the message to women that men are not to be trusted, they’ll just beat you up to get what they want. In option two again there is no redeeming virtue in the outcome; it is merely the lucky survive. Option three is perverse; the woman sacrificing to protect the man? Men don’t need protection from women; it is the other way around. Men are the ones who are strong and can function without support from women; it is the woman who needs to rely upon the man to fully express her feminine virtues and strengths. Option four is the winner; option four is the outcome that is beneficial to society. The man sacrificing for the woman sends a signal to all women that men will protect them even under the worst circumstances. This then leads to women trusting in men which then allows for good productive relationships between men and women to form.
On the side issue of a woman wanting her husband to shove the stranger woman into the water so that her husband can return to her safe and sound; of course from a selfish point of view this is what a woman would want. Would a woman want some stranger woman to die or for her husband to die? She of course would prefer the stranger woman to die because who is the stranger woman to her? The selfish interests of the man’s wife however are irrelevant to the moral dilemma of who should live and who should die on the sinking ship. When the moral question is simplified to whether it is the man or the woman who should die it is clearly the man who should die because from a societal point of view men are to protect women and not the other way around. The man dying creates the positive externality of sending a message to all women that men will protect them no matter what. The woman dying creates no similar positive externality. This is why the Chivalrous male duty extends to the sinking ship.