I can understand men wanting a place to go where they only get male company. I can understand the equivalent for females. No big deal. Muirfield is all male because it always has been and the current members don't see the need for any change. If and when they do see a need for change, as have most other golf clubs that used to have male only members, they will vote for change. I suspect that time will not be all that long in coming, but if it doesn't and if the club wishes to continue to isolate itself from other clubs (because they won't be allowed to host the Open Championships, for instance) that's up to them. There's nothing intrinsically wrong in being a bit isolationist, nor of being old farts, come to that.
Pressure may come from other parts of East Lothian because of business lost as a result of this club's unchanging attitude. That, I reckon, is what'll make enough of the old farts change their minds and vote to allow women members.