I'd like to start with two considerations:

  1. A lot of women (not all of them) explicitly say that the only difference between a flirt and a haressment is how attractive the guy is. Therefore, they do like attention but only from a very specific pool of men. That said, how are we men supposed to know whether we're that type or the creep ones if we can't read minds? To approach a girl, a man will always run the risk of being called a creep, no matter how respectful he is.

  2. A lot of men (not all of them) can't handle rejection and can become really agressive as a result.

With that in mind, wouldn't it be so much safer for women if they simply decided to start hitting on men? No more "creeps" hitting on women, because now women would go directly to the guys they wanted. However, i think it doesn't happen due to two main reasons:

  1. The majority of women don't have the slightest idea on how to initiate a sexual interaction with the opposite sex, as they never had to do so.

  2. They don't want to give away the power of rejection. It's much easier to be the ones who choose instead of the ones trying to be chosen. You can display some signals of interest (aka looking to the guy in a certain way, playing with your hair etc) and if he doesn't correspond, you can simply lie to yourself saying that you were not interest on him anyway. Now, if the roles were reversed, a rejection could be devasting for some women, as it would mean that they were not as attractive as they used to think.