UC-Irvine Law Dean and noted constitutional law scholar Erwin Chemerinsky critiques originalism, and several prominent originalists including Ilya Somin, Michael Ramsey, and Mike Rappaport respond. The argument they are most disdainful of is Chemerinsky's assertion that the constitution's exclusive use of "he" to refer to the President and Vice President indicates that only men can hold those positions under the original meaning of the document. "Uncharacteristically weak," declares Somin, while Ramsey labels the claim "preposterous," an argument "so poor I wonder if someone else wrote it and attached his name to it." They both contend that until quite recently "he" was used as a gender-neutral pronoun, so it is impossible to infer that its usage in the constitution was meant to render the executive branch gender exclusive.
While they may ultimately be correct, I think Chemerinsky's argument has more heft to it than they admit. It was of course common practice to use "he" as a general pronoun, though whether that was because it was understood to include women or because it was understood that women were not relevant to the conversation is less obvious. "He" in relation to political positions could just as easily stem from a widely shared understanding that women were not political subjects. Ramsey musters some intertextual evidence to support his position -- that when Article II, Section 1 delineates the necessary qualifications for a President it speaks of a "person" rather than a "man." And that has some persuasive force, but the problem is that the same archaic convention which allowed "he" to stand in for men and women also allowed for "person" to refer only to men. There are plenty of occasions where dead white men spoke of humanity or people with the assumption and understanding that it was only men about which they spoke.
More broadly, while it may be true that "he" could at the time have been understood to include both men and women, it also certainly could be used to refer only to men (how else would one do it?). Whether or not it was taking the former meaning or the latter is an exercise in interpretation, and one that depends on context. "Men" was similarly generic in character to "he" at the dawn of our nation, yet it is hard seriously contend that the phrase "all men are created equal" was meant to include women. Would citizens during the framing era have understood "he", in the context of who the Constitution contemplated could be President, to be inclusive of men and women alike, or just men? I would wager the latter.
Now arguably this doesn't close the door on originalist analysis of the clause's meaning. Arguably, the popular belief that "he" in this context referred to men and men alone was only the original expected application of the clause, not its original semantic meaning. This is a distinction Jack Balkin draws, and not all originalists accept his typology. But working off it for a moment, it's unclear. Words and phrases often can have very different semantic meanings at the same time period (for example, "hot dog" can mean either a tubular meat or a show-off). Where multiple meanings exist at a given time, is a generally understood consensus that one particular definition attaches in a particular context a case of "expected application" or "semantics"? Not an easy question, in my view.
This is not to say that Chemerinsky is necessarily right and his critics wrong. I'm not an originalist, so I hesitate to make definitive pronouncement on what results originalism yields (in part because I think they're often more indeterminate than its proponents would care to admit). But I think his point has more gravity than its given credit for, and citing the linguistic convention that "he" could have been in that era a gender-neutral pronoun does not actually get us that far.
UPDATE: Relevant to this discussion is an interesting history of gendered pronouns in the English language. Apparently the use of "he" as a gender neutral pronoun was first proposed in 1745, so it was certainly accepted by the time of the Constitution's drafting and probably understood as a possible meaning in the abstract, though again not necessarily in the context of who could serve as president.