Why do males have to woo the females and not vice versa?

No.12894323 ViewReplyOriginalReport
Nature, so as in human nature, follows the principle of "female choice" which just means that females are the ones deciding what males are worthy of reproduction.
However, there is something I don't really understand about this system. Why are men the ones to approach and ask out a girl while she is mostly subtle and passive about it? The vast majority of guys prove unworthy of reproduction anyway, so they get rejected. Why do girls not just go after the men they want and initiate everything? Wouldn't such a system be a lot more efficient?