The icy stare. If you are a male of nearly any generation, you have experienced it. You rush to open a door for a woman only to be met with a look that is cold and full of disdain. You wonder what you have done to merit a gaze which borders on hate. After all, you were just mimicking your father, just following your mother's advice, just being polite and considerate. But clearly, this person feels that your actions are inconsiderate, demeaning even. Since when, you wonder, did chivalry become sexism?
Fashion of the times
Since around 1970 is the quick answer, but when the change occurred is less interesting, and less important than why.
So, why did men open doors, offer an arm, order meals and generally treat women as vacuous, feeble, and less capable than themselves? The answer is fashion. And fashion is more than dress. It is custom.
Chivalry emerged in societies where women had neither economic nor social power. This fashionable weakening of their position required someone to look after them. Face it, if you can't own property, hold a meaningful job, or even walk alone in public without being thought a whore, your best bet is to hook up with a male who can offer some security. Women were, indeed, the weaker sex, but only because their position was made weaker by society, not because of any inherent weakness on their part.
A woman's reputation
Protection of a woman's honor was an understandable outgrowth of their weak position in society. If your primary means of survival was to attach yourself to a promising male, then an unsullied reputation became exceedingly important. And so, one of the foremost duties of a man was to guard the good name of the women in their lives. Failure to defend a woman's reputation meant a lifetime of economic and social hardship. It is easy to see why the chivalrous trait of protecting a woman's honor became a virtue in such an environment.