My baseless opinion: I think the key here is that women and men each tend to define themselves by their gender. You've heard the phrase, "He was a good man," etc. It's an identity thing. You are attacking their identity. "What a pussy" or "What a bitch" implies weakness that men are not allowed to have in most societies. That is why it is an insult. But a woman who is emotionally intelligent, caring, sensitive to the emotional hardships someone has, in most societies that is being "a good woman." Gender roles, and all that.
Women are supposed to be nurturers, many cultures would say, while men are supposed to be warriors. So, when you say a man has these feminine, nurturing, soft traits (which these cultures tend to VALUE in women), you are insulting the man's identity as a man. Likewise, in cultures like this, if you say a woman has a strong jaw and a stronger right hook, and imply she stinks like a man, wrestles like a man, and "has a bigger dick than Mitch over here," it's a backhanded compliment that insults her identity as a woman.
Take Brienne of Tarth, the character from Game of Thrones, for instance. She's a great warrior and takes pride in it. But she also has low self-esteem because she believes most men see her as a "great lumbering beast," with no feminine traits or beauty. Yes, she wants to be a great warrior, but she doesn't want to be thought of as just a man with boobs. A man who is seen as a "lumbering beast" is considered the ultimate expression of masculinity and is admired by men. A woman who is seen as a "lumbering beast" is seen as a joke among men or at most a strange curiosity.
And the reason for that, again, goes back to the gender expectations of society with cultures like these.
