The reason for this is that women are MORE SELECTIVE.

Think about it. Whenever there is a group of people deciding what to do, it's more efficient to have the most picky person decide, since their choice is most likely to be accepted by the other members. Otherwise everyone else has to work to find something the picky person will accept, and that's excess work.

Well that's EXACTLY what happens in the dating world. Women are more picky, but rather than take in upon themselves to decide who they want to date and act upon it, they more often expect the men to come to them, creating more work overall.

Let's use numbers to illustrate. Let's say (hypothetically) that a man will agree to date 20% of women, and women will agree to date 10% of men.

In this case, if a woman is looking to date, we would expect a match after she asks out 5 men she approves of.

If instead she makes the men do all the work, we would expect a match after 10 men ask her out.

Even a hybrid is more efficient than this. If the woman asks out 2 men, 6 men asking her out in addition are then required for there to be an expected match. That's 8 attempts, which is less than 10.

Clearly, in a world where women are more selective, allocating the work to men just complicates the process. Since women are the ones who have a narrower selection of potential mates, let them decide who they want, since they have a worse chance of being turned down.