If you have reasons why you think being a woman is worse than being a man, please do tell. There are some reasons being a female can suck, but when you compare the intensity of the problems between the sexes, men's problems outweigh women's problems by a ton.
Oh man.
Why even compare the problems? Why is it important? I don't know what it's like to be a man, so I don't dare make the statement, "Women have it worse." What makes you think you have the right to compare when you have never been a woman?
I'm a woman with SAD. I'm a woman with AvPD, actually. Men don't flock to me. I've never had male friends, let alone a boyfriend. I'm not ugly or disfigured. I'm not beautiful either, but I am attractive to some. But they still do not throw themselves at me. Why do you have this notion in your head?
Even if women were the dominating sex and were expected to go after men, what makes you think that would get rid of your SAD? After filtering out all the women who just want to get into your pants, you would find a couple decent relationships. But all of them would be terrible rocky--some would enhance your anxiety. Some would crumble because of your SAD and would leave you feeling like a failure.
The problem isn't that society dictates that men should ask women out. This isn't the 50s.
The problem is, and will always be, your SOCIAL ANXIETY DISORDER.