I've already addressed that "problem." It's answered in a single word: "Election." There was a war going on, and all persons were put to choice of allegiance. Minors were deemed incapable of making that election until the lapse of their minority. So even though born on the soil, they were effectively bound by the election decision of the parent. Once the war is over there is no obstacle posed to their common law birth citizenship.
Story explains this, speaking first about "the general principle of common law," but then noting "But a case of more nicety and intricacy is when a country is divided by a civil war and each party establishes a separate and independent form of government." He later adds: "The case of the separation of the United States from Great Britain is perhaps not strictly brought within any of the descriptions already referred to, and it has been treated on many occasions, both at the bar and on the bench, as a case sui generis.
Look up sui generis. War presents its own special conditions and rules that don't operate otherwise. Your fallacy here is trying to argue the special case to defeat the general rule. That won't work.
My fallacy is in thinking that there is any point to arguing with someone who as Reagan said:
"Knows so much which isn't so."
I suppose I do it for amusement. It is a sadistic streak out of which I really ought to grow.