A while back I posted on Hume's sexist argument against immortality of the soul - i.e., the argument to the effect that if the soul were immortal as Christians think it to be, women would have mental faculties equal to those of men, so the soul can't be immortal. I couldn't think of another case of blatant sexism (he treads close in discussing chastity, but it's a bit obscure what he intends there), but came across one today when reviewing various things Hume says on good manners. The topic is the rise of gallantry in civilized societies:
"As nature has given man the superiority above woman, by endowing him with greater strength both of mind and body, it is his part to alleviate that superiority, as much as possible, by the generosity of his behaviour, and by a studied deference and complaisance for all her inclinations and opinions. Barbarous nations display this superiority by reducing their females to the most abject slavery; by confining them, by beating them, by selling them, by killing them. But the male sex, among a polite people, discover their authority in a more generous, though not a less evident manner; by civility, by respect, by complaisance, and, in a word, by gallantry."
(This is from the essay "Of the Rise and Progress of the Arts and Sciences," par. 40.) If you hadn't figured it out before, now you know why there have been feminists opposed to things like men's opening doors for women: they are trying to stamp out Humean tones in gallantry, in which the thought is that men must do nice things for women because women are weaker and more stupid; in which gallantry is just a way for men to exercise authority over women without the nasty business of slavetrading and killing; in which the idea is that men must be polite to women so that their being inferior isn't such an unpleasant thing.
Fortunately, there is more to Hume on manners than this; I'll be posting on the better parts this week.
