When you become a naturalized citizen you take an oath in Public:
The oath of allegiance is:
"I hereby declare, on oath, that I absolutely and entirely renounce and abjure all allegiance and fidelity to any foreign prince, potentate, state, or sovereignty of whom or which I have heretofore been a subject or citizen; that I will support and defend the Constitution and laws of the United States of America against all enemies, foreign and domestic; that I will bear true faith and allegiance to the same; that I will bear arms on behalf of the United States when required by the law; that I will perform noncombatant service in the Armed Forces of the United States when required by the law; that I will perform work of national importance under civilian direction when required by the law; and that I take this obligation freely without any mental reservation or purpose of evasion; so help me God."
I understand the importance of allegiance within the concept of citizenship (although, it should be noted that individuals who are born citizens are not required to say any oath of allegiance). I’m simply stating that a child born in the U.S., regardless of parentage, is (by law and by the 14th Amendment) a citizen of the United States - though we fought against the British, in part to free ourselves from their concept of natural-law subjects-by-birth, we do, nonetheless, retain a form of birthright citizenship through the 14th Amendment.