When Jefferson composed the phrase: "...that all men are created equal..." do you think he meant to include women? Or, at the time, did he consider women unequal to men? Why should we take his meaning of men to include women?
If he meant to include women, why wasn't the term "humans" or "people" used instead? Franklin tweaked Jefferson's wording for the final DOI and so he might have thought to include women, but he didn't either.
In 1776, were women equal to men in every regard? No. So do you agree that these Framers were very specific in choosing their words for these important documents?
But no - according to most views of the law back in the 1700’s women were inferior to men according to natural law.
Our view of natural law has changed, and equality under the law means that men and women are to be treated equally under the law.
Thus U.S. law is to always reflect our best understanding of natural law - and it is NOT the natural condition of women to be unequal and subservient to men - despite the protestation of most 18th century men otherwise.
As to what the term “natural born citizen” meant at that time - under English law the children of foreigners born in English territory were “natural born” - so the meaning as known and understood by our founders would not be confined solely to the children of citizens.
Vatell’s reasoning would not grant citizenship at birth to the children of foreigners born on the soil. It is not that he would grant them citizenship of a lesser kind at birth. They would not be citizens at all.