Was there some statute or other law a century ago that said only males could serve as president? If so, when did that change (if in fact it did)?
The language argument about the constitution is that the Constitution uses the pronoun "he" in referring to the president – they would not have used the construction "he or she", or "s/he". Article I also uses "he" to refer to qualifications of representatives and senators (residency, age). Then in creating the office of predident pro tempore of the Senate, it uses "he" to refer to a Vice President who is exercising the office of President of the United States. In Article IV Section II it states:
A person charged in any state with treason, felony, or other crime, who shall flee from justice, and be found in another state, shall on demand of the executive authority of the state from which he fled, be delivered up, to be removed to the state having jurisdiction of the crime.
Thus women cannot be extradited, if the "'he' means male" theory prevails.
In 1872, Victoria Woodhull ran for president, and while it is true there were questions about her eligibility, that was because of her age rather than sex. Belva Lockwood ran for president in 1884 and 1888. This is not strong enough to constitute proof that being female was not a bar to holding the office, but it is indicative of that conclusion. The strongest evidence that the use of "he" in the Constitution had no significance is the fact that Jeanette Rankin was elected US Representative from Montana in 1916, 2 years before Congress approved the 19th Amendment.
Since the only way to impose any restrictions on the presidency is via the Constitution (i.e. Congress can't pass a law redefining the qualification for office), and since the use of "he" has never been strictly interpreted to preclude female senators and representatives, we have to conclude that there never has been a prohibition against a female president.
The first lady is not part of the legal line succession for presidency in the United States, and she never has been. Throwing in Wilson and suffrage is all relatively moot. There's no need for any "formal" statute which states specifically that one single individual is ineligible.
The gender of the president's spouse has little to do with anything. The First Lady is not a formally elected nor appointed government official and therefore ineligible. The US could have a female president and the "first man" would be equally ineligible.
1 Vice President
2 Speaker of the House of Representatives
3 President pro tempore of the Senate
4 Secretary of State
5 Secretary of the Treasury
6 Secretary of Defense
7 Attorney General
— Secretary of the Interior 8 Secretary of Agriculture
9 Secretary of Commerce 10 Secretary of Labor
11 Secretary of Health and Human Services
12 Secretary of Housing and Urban Development
13 Secretary of Transportation
14 Secretary of Energy
15 Secretary of Education
16 Secretary of Veterans Affairs
17 Secretary of Homeland Security