Your article is good timing considering Congress has been considering updating the Selective Service law to make women eligible for the draft if it ever returns, and to make registering for the draft an automatic process rather than a voluntary but legally required one.
The effort started out bipartisan, just a way to bring draft registration into the 21st century. But it has stalled because certain conservative figures in DC are making big political hay out of women registering. Looks like the new law doesn't have a shot, even though it's not actually about drafting women.
Just the future possibility was enough to panic patriarchs.