While it's true, more women register Democrat, that doesn't mean "women are fleeing the Republican party in droves." The number of women who register republican has been largely the same.
But I understand your confusion. It's much easier to make a claim with no research than it is to do research and then make informed conclusions.
https://www.people-press.org/2016/09/13/2-party-affiliation-among-voters-1992-2016/