The Argument put forth is that American law is based on English Common law. The laws of Canada are most certainly based on English Common Law. If the source of both nations is English Common Law, then you have a ridiculous situation where two nations, using the same source of authority, lay claim to the same man.
“Common Law” is a theory in jurisprudence where greater weight is given to precedence under the concept that it is unfair to treat similar facts differently on different occasions. It is one of the three forms of law; common law, statutory law and administrative law.
It is "unwritten law" that is established by long usage and habit rather than by legislative statute. The Jus Soli argument for the United States is based on the notion that we adopted English Common law as regards our citizens.
The British body of precedents (rulings) is different that the US body of precedence. A US court is expected to follow US common law and a British court is expected to follow British common law.
You appear to be somewhat new to this discussion. The Dominant argument on the Jeff Winston side of the issue is that US citizen Law = English Subject Law, except for the "perpetual allegiance" part. Why they keep trying to cut that part off, I do not know. Perhaps because it really bollocks' their argument?
Really, have you ever studied law?
For many years. Have you ever studied Engineering? It is a jarring transition to go from pseudo logic and reliance on previous "opinions" to accurate measurement and calculation. Of the two systems, one can continuously produce ridiculous and catastrophic results, and still be regarded as operating within acceptable margins by it's adherents.
If Buildings were Built in the manner that laws are adjudicated, the first woodpecker which came along would destroy civilization.
Neither Canada's nor the US's citizenship determinations take their authority from English common law. They are based on statutory law or, in cases covered by the 14th Amendment (and possibly some Canadian cases; I don't know their constitution), constitutional law.
The Jus Soli argument for the United States is based on the notion that we adopted English Common law as regards our citizens.
The jus soli argument for the United States is based on the black-letter law of the Fourteenth Amendment. It's becoming increasingly clear that you lack the first clue about how common law works; it does not supersede statutory law.