One does not have to be "subject to the jurisdiction" at all times. You can be subject to the jurisdiction of the country you're temporarily in. Local police can arrest you, you can be prosecuted by local authorities in local courts, and you then go to local prison. That doesn't mean that if you return to your home country, you couldn't also be prosecuted there, if their laws are written that way. You are conflating the two senses of the word "subject", by insisting that "subject to the jurisdiction thereof" incorporates the meaning of "a subject of". Check out Websters 1928 Dictionary for examples of "subject to" -- quite normal and ordinary usage. Just because Bouvier's only defines the noun, doesn't mean that was its only or most frequent usage.
I am not arguing that slaverly wasn't perfectly legal in this country. I am saying that kidnapping someone and transporting them against their will to another country does not automatically strip them of their citizenship, and bestow upon them the citizenship of their "host" country. If that were so, someone kidnapped in Bosnia, or Zambia or Pakistan, and transported to Guantanamo would automatically become an American citizen. Or Cuban, if you prefer. As the Fourteenth Amendment says, if you are born in this country, and you are subject to the jurisdiction of this country (meaning not immune, such as diplomat or child of a diplomat), then you are an American citizen.
There are many people in this country today who don't know the origins of their forefathers, not even if they were legal immigrants or not, and America is the only country they've ever known. (Many immigrants changed their names, and invented new stories for themselves when starting a new life). So are you saying they shouldn't be Americans? Even if their parents were born here? And their parent's parents? If it's just a matter of multiple generations, or passing of time, or ignorance of your origins, how many generations? How much time? How much ignorance?
I'm afraid I don't have access to that particular dictionary, but I looked it up on Merriam-Webster Online, and the first definition that came up for the adjective (not the noun) was, "owing obedience or allegiance to the power or dominion of another". So there's a difference between being subject to a government's jurisdiction, and simply being expected to obey its laws. People who are only visiting this country don't owe any allegiance to it.
And looking at the clear intent behind what was going on can only clear it up further. The well known reason for the 14th amendment was to protect the freed slaves, and in particular, to reverse the holding in Dred Scott that blacks can't be citizens. There's no evidence that Congress intended to come up with a whole new theory of citizenship to take the place of the one that had been in effect up to that point. To read it the way you're reading it, no person born in this country could ever even voluntarily renounce his citizenship.
If that were so, someone kidnapped in Bosnia, or Zambia or Pakistan, and transported to Guantanamo would automatically become an American citizen.
Except that our laws don't provide for such a thing, the way they stripped slaves of citizenship of their countries of origin.
There are many people in this country today who don't know the origins of their forefathers, not even if they were legal immigrants or not, and America is the only country they've ever known. (Many immigrants changed their names, and invented new stories for themselves when starting a new life). So are you saying they shouldn't be Americans?
How could you possibly conclude that? My point is that it does make them Americans, and by all rights, should make them citizens. The 14th amendment simply took that moral principle and made it the law of the land.
The basic idea is, if someone comes to this country, or is brought to this country, and is no longer considered by our laws to be subject to any other country's jurisdiction, and then he has children here, those children are subject to our jurisdiction, and are citizens of this country.