There is some secret courting dance the male must do at that point, and I don't know it.

Ok, obviously there are some men ("non-neurotypical") which find this part difficult. But my point is that the "secret courting dance" is not some mind manipulation dark ritual.

I once threw a party and invited only random strangers, where every single person who attended hooked up with another stranger, except me and my co-host. We left 2 dozen strangers silently locking jaws in pairs in our apartment and went to another party.

Maybe you should have considered inviting more women than men :D