Comparing average man vs average woman salary is not quite analogous.
In USA men and women do not necessarily have the same experience (women often take time off to care for kids) and often do not get the same types of degrees or specialize in the same types of fields. Women often work lower-paying careers. And there are other variables that make it somewhat misleading to just plop the two averages next to each other.
So if you compare a male software engineer with a female software engineer (or male nurse with female nurse), with the same job title and number of years experience, I think the discrepancy goes down somewhat, although it is still present. I have also read that a part of this difference is that women are less likely to ask for a higher salary than men. So I think that would narrow the gap as well. But would the two hypothetical salaries be equal at that point? That would be an interesting question.
Anyway this is an issue overall, and I'm sure at the White House as well. It does seem encouraging that gap is narrower at the White House than nation-wide, whatever that implies.