And since two answers here rely on the interpretation of pronouns in the Constitution... that's also an argument but not an incredibly convincing argument, alas. The election of the first woman to Congress did precede the 19th amendment, but not by much... and a law review around that time pointed out that courts tended interpret the ambiguity against women (alas without providing examples when it comes to candidacy.)
III. HE/HIM/HIS
All pronoun references to the President, the Vice President, Senators and
Representatives, and other officers are masculine. Some version of a male pronoun
appears close to 50 times in the Constitution. Indeed, the qualifications for electors
in the Fourteenth Amendment is specifically stated as “male.”
Use of the male pronoun to refer to all humans, according to linguist Dennis
Baron, can be traced back as far as the Latinists of the sixteenth century and was
widely accepted in the eighteenth century. Women seeking voting rights argued
that, if the male pronoun was general to all sexes, its exclusive use in suffrage
statutes could not pose any impediment to the suffrage of women. Equally, they
argued, it could not bar women from being able to take up elected office. A note
in the Harvard Law Review in 1910 summed up the chauvinism of the time, stating
that “although the exclusive use of masculine pronouns in the constitutions in this
country has never been regarded as excluding women, there has been little
tendency to construe general provisions in their favors.” The article went on to
observe that contemporary courts had tended to construe any ambiguity against
female office-holding.
That attitude did not seem to deter Sara Platt Decker of Denver, Colorado,
however, who considered a run for Congress in 1909. Speculation about a female
congressional candidate sparked one opinion writer to object — “[s]trict adherents
to the letter of the Constitution maintain that the presence of the masculine
pronoun, and the absence of any other, obviously renders ineligible any person of
the feminine persuasion.” It seems, however, that this writer held a minority
view. Jeanette Rankin, of Montana, became the first elected female congress
member in 1916 – four years before ratification of the 19th Amendment. And,
although there was a bit of grumbling by sources to the Washington Post about
pronouns and Montana’s new representative, her swearing in took place without
much pronoun based objection. By 1922, the idea that she could have been barred
from office because of pronouns barely merited a sentence in Joseph Ragland
Long’s treatise on American Government: “[T]he pronoun ‘he’ [in Article I]
includes both sexes.”
Today, the assumption that “he” means “he or she” has become so
entrenched, that when former Senator and Secretary of State Hillary Clinton ran
for President in 2015, no one in mainstream legal circles attempted to argue that
she was ineligible for the Presidency.
Although these case have been basically forgotten by now, the original 1910 article (Note, Eligibility of Women for Public Office, 24 HARV. L. REV. 139, 140 (1910)) provides some examples in which the lack of voting rights was interpreted as extending to lack eligibility:
Most constitutions
restrict suffrage to males, and even where eligibility for office
is not expressly confined to electors, it would seem naturally to be
predicated on the right to exercise this primary governmental function.
On this ground, several cases have denied women the right to hold
office.
[footnote:] See Atty.-Gen. v. Abbott, supra; Atchison v. Lucas, supra. But see State v. Hostetter,
supra; Wright v. Noell, supra. It has been said that conferring suffrage on women
makes them eligible for office. See State v. Cones, I5 Neb. 444. Cf. Olive v. Ingram,
2 Strange III4. But in England it has been held that a woman is not eligible even
for an office for which she can vote. Beresford-Hope v. Lady Sandhurst, supra.
So the all-inclusive male-pronoun was hardly that convincing before the 19th Amendment.
