In Death of a Salesman, there is a lot of putting down women and treating them like second class citizens. There are some examples of this in the story, especially with the characters of Happy and Biff. Since they are so immature, they are unable to establish meaningful connections with females and instead (as in the restaurant scene) they go for cheap and easy women to kill some time with.
Willy's character always treated people in general like second class citizens thinking that he was always liked, and it was obvious that he did not treat his wife with the highest of respects when he took a mistress.
NONE of these things, however, have to do with male pride. Male pride does NOT involve putting women down. Male pride may result in a man feeling shame for something they are unable to do as expected by society, but male pride has nothing to do with putting people down. If anything, male LACK of pride is what does that.