From your excerpt: The fourteenth amendment of the constitution, in the declaration that 'all persons born or naturalized in the United States, and subject to the jurisdiction thereof, are citizens of the United States and of the state wherein they reside,' contemplates two sources of citizenship, and two only,-birth and naturalization.
Incomplete. Using a single source to define US citizenship ensues confusion. Generally speaking, US citizenship can happen in 3 ways; place of birth, by blood, and naturalization. Any one of these can bestow US citizenship, but it may not make one a natural born citizen.
The Constitutional framers were obviously worried of loyalty to the country. Natural born in the strictest sense is being born within the United States to US citizens is what the framers had in mind. Being born to foreigners or overseas may produce a person who has split his loyalty among nations, and clearly the Framers wanted to avoid that person from becoming president. However, the question of natural born citizen has not been addressed by the Supreme Court.
Nope. What you are missing is that "natural-born citizen" had a specific meaning in common law. Most of the Founders were lawyers. They knew exactly what it meant. There was no need to define it in the Constitution, as it already had a specific meaning.
Don't take my word for it. Read the Wong Kim Supreme Court decision. The Court explains what these terms mean and their history in tens of pages of detail.
Don't argue with me. Argue with the Supreme Court.