This may seem as an odd question, and it is. But it is a good question in light of the current US presidential elections and LGBT in general.
If gender is a social construct, then people can be man or woman (and in some cases both, or neither) depending on their subjective views.
Caitlyn Jenner, formerly Bruce Jenner and father of six children, is a well-known recent example. He, or rather she, has been called the most famous transgender woman in the world.
What makes us think that Hillary Clinton is a woman and not a man? Is Hillary Clinton a woman despite her subjective views or in spite of her subjective views? If Hillary Clinton announced tomorrow that she is a 'he', then would Hillary Clinton be a woman candidate or a man candidate?
And if president Barack Obama announced tomorrow that he is a 'she', then would there be a woman president in the White House?