This might seem like an odd question, but a journalist recently asked me my opinion about the matter. It turns out that Article II of the Constitution refers to the President as a him. For example: “He shall hold his Office during the Term of four Years.” If this “he” meant only a male person, there would be a strong argument that the President had to be a male.
But I believe that this interpretation is mistaken. It is my understanding that the term “he” at the time of the Constitution had multiple meanings or usages. While one of those was to refer to a male person, another was to use the term “he” to mean “he or she.” Under that usage, a female President would be constitutional.
The same issue arises as to members of Congress as well. For example, Article I, section 2, clause 2 provides “No person shall be a Representative who shall not have attained to the Age of twenty-five Years, and been seven Years a Citizen of the United States, and who shall not, when elected, be an Inhabitant of that State in which he shall be chosen.” (Emphasis added.)
There are strong reasons for preferring the “he or she” meaning over the “he” meaning. Most importantly, the Constitution contains explicit qualifications for serving in Congress and in the presidency. These are normally thought to be the exclusive qualifications set by the Constitution. Reading in another qualification – maleness – would thus conflict with the constitutional structure.