I think it's associated with the chivalry that guys would undergo to ask permission from a woman's father. Since those days are over, I don't think women like to be chased at all. In fact I think they HATE it.

They would much prefer to throw themselves at alphas. Any beta male in his right mind should go MGTOW until he becomes an alpha himself.

If they like being chased, they like the illusion of being chased.