Au contraire, folks.
First, a woman is entitled to precisely equal treatment as a man – no more and no less. Neither paternalistic decisions about what she may or may not do nor special consideration for sexist reasons. She may be privileged to have courtesies and chivalric treatment shown her. This is something offered by men, both as a social “lubricant” (etiquette is a means of greasing the squeaky joints in interpersonal relationships) or as a mild form of courtship.
However, there is a quite practical survivalist reason for women and children first – racial survival. Granted that in an overpopulated world this does not obtain, for most of human history, when genetic and cultural traits were being evolved, it did. And the logic is quite simple: for a man, a half hour of pleasurable effort will suffice to engender a child; for a woman, it’s nine months of ongoing effort. Then the child must be raised from helpless infancy to a point where it can be a contributing member of the society into which it is born – and this too has devolved largely on women historically. Not to minimize the importance of a father to functional human psychological growth, but one parent, normally the one giving birth, must be present or someone in loco parentis function in the same means, for that child to survive its first few years.
As a mental exercise, suppose eleven people in a spaceship crash on an uninhabited planet far from anything else. Hope of rescue is effetively nil. By sheer luck, they have all the materials and skills they need to survive and the planet is nor merely hospitable but absolutely welcoming to human life. In addition, neither scruples nor homosexual orientation is present in any of them to prevent sexual reproduction, all are fertile and philoprogenitive (want children), and none of them are possessively jealous. The object is to be fruitful, multiply, and subdue the planet.
Okay, we have one woman and ten men. Results: twenty children at maximum in the second generation, and that only if she starts young and remains constantly pregnant insofar as possible.
Now, one man and ten women. Results: nearly a hundred children in the second generation without enormous strain on the women. (This assumes each averaging ten children, high for today’s society, but not unreasonable over a 25 year span in this pseudo-ideal situation.)
We recognize that in each case there is a strain on the gene pool and that the second generation will all be half-siblings, but ignore these problems for the nonce.
Extreme example, but the point is clear: for the future survival of a species equipped like ours is, protection of the child-bearing sex, even at the expense of a substantial portion of the child-begetting sex, is a survival trait.