It's not. This is a straw man. Nobody said that all citizens are "natural-born citizens." Naturalized citizens are not "natural-born citizens," and therein lies the distinction.
Regarding your argument that English common law is an inappropriate method of defining "natural-born citizen," riddle me this, then: Where did Chief Justice Waite look to define "natural-born citizen"?
The Court's opinion in Minor was unanimous; there were no concurring or separate opinions. Moreover, the first two sentences of the above quote spell out exactly what the problem y'all are having is. First, "natural-born citizen" isn't defined in the Constitution. As a consequence, second, we need to pick a source to define it. Some of y'all insist that this source has to be a specific French-to-English translation of a Swiss legalist's writings (i.e. de Vattel's Le Droit des Gens).
But Chief Justice Waite's words, which I quoted verbatim, are all I need to disprove your argument. He did not resort to de Vattel, either in the original French or in that specific French-to-English translation; in fact, de Vattel isn't cited at all throughout the entire opinion. No, Chief Justice Waite sought out COMMON LAW as a means of defining "natural-born citizen."
Mason was highly influential in the era, the intellectual equal or better of any man present, and so his resistance was a problem. Madison sought to bridge the impasse, working as a mediator between Mason and others. The very first amendment, proposed practically immediately following ratification, brought Mason's Bill of Rights to pass. Madison is often credited, but credit belongs to Mason, who put his reputation and lifelong friendships on the line, as well as his place in history.
To the extent that the old English common law is represented at all in our Founding documents, it is to be found there, in the Bill of Rights. The remainder overturned the old common law. It's that matter of negative rights versus positive rights, one that has been acknowledged over the intervening centuries.
The common law to which Waite referred clearly was not English. That is evident from the language of the cite regarding natural born citizens from Minor v. Happersett. Your argument fails on this point. Perhaps you meant to refer to the cite of Minor from Horace Gray's ponderously improbable and wholly unnecessary tour of western civilization known as Wong Kim Ark.
References: