I used to have crushes and I also know other women who pursued men. Anyway, despite how I know many women who did this, none of them had a happy outcome. They guy either dated the girl as some placeholder girlfriend, continued flirting as he saw her as boosting his ego for free, ignored her, distanced himself away from her, rejected her, or hinted he was actually taken to encourage the girl to back off herself. So yup, it was a matter of either being used for sex or attention or losing face. None of it is beneficial for women.

I guess some users here wish they could take initiative as they don't like being passive and want to be in control of making a relationship happen, but I like to think if it's meant to be, the relationships will naturally happen. If he wanted to, he would.